Why dont they teach this in all schools... we are just told to memorise the formula, without any hint of understanding whatsoever... Thanks Eddie, you just helped out a lot, as always!
Right! My teacher taught me the Quadratic formula (Here it’s called the abc-formula for some reason) and he just told me to remember that D = b^2 - 4ac and that x = (-b + sqrt(D))/2a or x = (-b - sqrt(D))/2a. God knows why I had to do that. Me, being a student who’s having a bit of a struggle with math at times, I believe, needs to *understand* the formula.
Yeah, I had the exact same, with the D=(....), we called it the greek "delta", though. And its not just for struggling stidents, I'm not bad at maths, it has always been my favourite subject, but actually *understanding* the formulas is priceless, because you remember them more and know how they work.
We were given this as an extension for some of the more talented mathematicians in year 9 (UK). It really helps your understanding and you learn why it is applied in that way
I got really confused by that because My headset is broken and if the wire is not in properly the audio cuts out so I am sitting there trying to readjust the cable every second thinking my headset has had its full life so thank you for mentioning this XD
I like the way he shows every step without skipping anything. Sometimes doing things like, "I am going to do this and this" confuses students because they have to think about two manipulations at once. He actually separated the square root on the right before taking the square root of the denominator. Excellent teacher.
why doesn't he have to say + or - the a when he takes square root of the a^2 at the end!? He said plus or minus for the big part that he takes square root of, but when he gets to square rooting the a^2 at the end, he doesn't do another + or - !
@@MathCuriousity + or - applies to the entire fraction. The 4a^2 there is a denominator and when you get the square root of it, it just stays as it is, just 2a. It's just normal addition and subtraction of fractions. The numerator is sqrt(b^2 - 4ac), the denominator of it is 2a. The numerator of the other fraction is -b, the denominator of it is 2a as well. They have the same denominator, and thus they can combine. Plus minus is two operations, addition and subtraction. If you're talking about plus-minus in the denominator, well here's the thing. If the denominator is negative and the numerator is positive, the whole fraction is negative. If the denominator is negative and the numerator is negative, the whole fraction is positive. If the denominator is positive and the numerator is positive, the whole fraction is positive. If the denominator is positive and the numerator is negative, the whole fraction is negative.
Starting with a pickup line, "formulas have a ...." making jokes, having fun, this guy made a math class seem like English, so darn easy and fun! I can't believe these kind of teachers existed in past..
I remember reading this from the Math book in 8th grade and it was great to see the original equation becoming the formula that the teacher told us to use without knowing why. I must be the only kid who cared to know back then And congrats to the Professor
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
60 years ago during my mathematics GCE 'O' level I derived the formula on scrap paper because I could not remember the formula but I did understand where it came from.
The quadratic formula has been one of my favorite formulas and I never understood how it related to a quadratic equation. None of my math teachers ever took the time to show WHY it works, just told us to use it because it worked.
Hi Eddie, this is a "pre-viewing comment", I'm about to show this video to my very bright Year 9 class. One of your videos really helped me with Logs, so I'm giving you the chance with my Year 9 🙂
It might be the video's age, but the sound goes out at random times. I tried showing this to my class last week, but the sound breaks proved to be a large distraction for them. Great video otherwise
Well, not only did my class love the video, it's really strengthened my knowledge of this topic. I've subscribed, I hope you are looking into getting monetised, us teachers deserve every penny we get! I think some of my class have subscribed to you.
A minor point. Radical 4a^2 is not necessarily 2a. It could be -2a if a is negative. It doesn't affect the final solution, but we shouldn't ignore this issue.
i know this is a few years late but ill share this anyway, that is actually a common misconception! the plus and minus only applies to: x^2 = 4 x = ± √4 x = ± 2 but in radicals, √(a^2) = |a| so √4 is always just 2 (called the principal root), even if √4 can be written as √ [(-2)^2], it is equal to |-2|, thus it's still just 2. It can only become -2 if it is indicated with a negative sign outside the radical, i.e. -√4. Hope this was helpful! xx
i still dont get the step at 4:20...why do we divide it by 2 and then square it? What is the purpose of doing that and is there a rule telling us to do that? I dont remember ever having to divide anything by 2 and squaring it in all my math experience
Say you had x^2-2x on the LHS. What you always have to do when you have something like this is to half the coefficient of x, then square it to get x^2-2x+((1/2)×(2))^2 = x^2-2x+1 = (x-1)^2. It's because the middle term is always twice the (square root of) other terms multiplied, e.g. x^2+6x+9 (9 =3^2) = (1)x^2+2(1x)(3)+3^2 (ax+b)^2 = a^2x^2+2abx+b^2
Because there isn't another b^2 in the second half of the term under the square root. There is no b^2 in the term -4*a*c. You cannot factor sqrt(x^2 - y) as x*sqrt(1 - y), so you cannot do the same with sqrt(b^2 - 4*a*c). In the special case that c=0, then the b^2 does do exactly what you are asking for. One might also think that a could equal zero for the same thing to happen, and they would be somewhat correct. But if a=0, then the entire denominator would equal zero, which cannot be. We'd also not even have a quadratic, as we'd have a line.
Would someone explain why he have to say + or - the a when he takes square root of the a^2 at the end!? He said plus or minus for the big part that he takes square root of, but when he gets to square rooting the a^2 at the end, he doesn't do another + or - !
I have a question. In 8:51, wouldn't it be square root of 4a^2 is positive or negative 2a? Cause we always consider negative when looking for square root right?
Yes! You are right. This is a quibble I have with all the derivations of the quadratic formula. They all ignore this point. At the end it doesn't matter +radical(b^2-4ac)/(-2a) = -radical(b^2-4ac)/2a. And -radical(b^2-4ac)/(-2a) = +radical(b^2-4ac)/(2a). So at the end we still get +-radical(b^2-4ac)/(2a). The order just gets changed, but we don't care about the order. But a way to clean this up is by to first multiply both sides by 4a^2 before taking square roots. 4a^2(x+b/(2a))^2 = b^2-4ac (2a(x+b/(2a))^2 = b^2-4ac Now we can take square root and avoid this issue: 2a(x+b/(2a)) = +-radical(b^2-4ac) etc... Now the issue of the sign of a doesn't matter.
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
qiankun danuoyi, it comes from the process of completing the square. See this video where Eddie explains this process geometrically. He starts explaining the "b/2a" part at 1:10. czcams.com/video/McDdEw_Fb5E/video.html
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
yes when you factorise a quadratic you can have that, however when you are solving one you can just divide the whole quadratic by a and divide 0 by a to make it easier and it will still work
Leo Callebaut, b/2a comes from the process of completing the square. See this video where Eddie explains this process geometrically. He starts explaining the "b/2a" part at 1:10. czcams.com/video/McDdEw_Fb5E/video.html
@@Isomnophilia You're welcome. :) Visual explanations like that really help to intuitively understand what you are doing and why as opposed to just memorizing formulas. I never got that kind of intuitive explanation in school, but is great that there are so many amazing lessons available now on the internet.
@@Tekkerue this is the future of teaching. Subscribing to qualified teachers for quality material. Conferencing / VR / instant referencing... resources are there to create virtual schools eventually.
@@Isomnophilia Yeah, there are already college courses available online from universities like Stanford, Harvard, MIT, etc where you can watch full videos of the course lectures and some of the courses even have homework assignments too so you get the whole course for free. Pretty cool! :) Then there are amazing CZcams channels who are not accredited teachers, but they do an amazing job teaching the material, like 3Blue1Brown who is seriously in a league of his own. It's only a matter of time before that "piece of paper" becomes essentially worthless because people can get a better education through resources online rather than sitting in a classroom with a crap teacher who can't teach the material even half as well. lol
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
If a were equal to zero, you wouldn't even have a quadratic equation in the first place; you'd have a linear equation, and you wouldn't need to even think about this formula.
Good news!!!!!!!!! Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah. Acts 3:19?-?20 CSB From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.” Matthew 4:17 CSB “The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!” Mark 1:15 CSB Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God. John 3:3?, ?5 CSB Whoever claims to live in him must live as Jesus did. 1 John 2:6 NIV 1john.bible/1-john-2-6 Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me. John 14:6 CSB For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life. John 3:16 GNB bible.com/bible/296/jhn.3.16.GNB _Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world. Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins. You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world. Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God. Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour. Repent, turn away from your sins and live because, *_Jesus Lives_*
It's the third time I've been seen a video from Mr. Who about Quadratic formula derivation and I still pull out my hair when he straightforward takes the square root of the second member before even assuming b²-4ac is non negative... Actually the formula is correct if and and only if b²-4ac is non negative. And magically (luck or wellc chosen examples) all the examples he gives are Delta positive. This is really important to notice the case Delta < 0 because it might be tricky when students will face a non positive delta...
Eddie does talk about cases with delta < 0 later on, which is recorded on other videos. There is no need to talk about everything at once, it's better to teach stuff gradually. Besides, the formula is always correct, even if the discriminant is negative, you just have to look outside of real numbers.
Never fully got this in 1992. Now I finally understand it🥹 And yes, better math teachers slow down and explain each step because it’s a lot of steps. Perfect!
Why dont they teach this in all schools... we are just told to memorise the formula, without any hint of understanding whatsoever... Thanks Eddie, you just helped out a lot, as always!
Those are mostly A level i think or if your aiming for A* or 9
Tenshi - True, but I take that sort of course, and the bulk of it is still memory
Right! My teacher taught me the Quadratic formula (Here it’s called the abc-formula for some reason) and he just told me to remember that D = b^2 - 4ac and that x = (-b + sqrt(D))/2a or x = (-b - sqrt(D))/2a. God knows why I had to do that. Me, being a student who’s having a bit of a struggle with math at times, I believe, needs to *understand* the formula.
Yeah, I had the exact same, with the D=(....), we called it the greek "delta", though. And its not just for struggling stidents, I'm not bad at maths, it has always been my favourite subject, but actually *understanding* the formulas is priceless, because you remember them more and know how they work.
We were given this as an extension for some of the more talented mathematicians in year 9 (UK). It really helps your understanding and you learn why it is applied in that way
Audio keeps cutting out :/
***** Nah you're alright! The most important thing for me as a viewer is looking at the whiteboard to see how certain things are done.
Thanks anyway.
so it wasn't just me
I thought that there's something wrong with my computer
I got really confused by that because My headset is broken and if the wire is not in properly the audio cuts out so I am sitting there trying to readjust the cable every second thinking my headset has had its full life so thank you for mentioning this XD
Oops! I already ordered new headphones from amazon. My bad
I like the way he shows every step without skipping anything. Sometimes doing things like, "I am going to do this and this" confuses students because they have to think about two manipulations at once. He actually separated the square root on the right before taking the square root of the denominator. Excellent teacher.
why doesn't he have to say + or - the a when he takes square root of the a^2 at the end!? He said plus or minus for the big part that he takes square root of, but when he gets to square rooting the a^2 at the end, he doesn't do another + or - !
@@MathCuriousity + or - applies to the entire fraction. The 4a^2 there is a denominator and when you get the square root of it, it just stays as it is, just 2a. It's just normal addition and subtraction of fractions. The numerator is sqrt(b^2 - 4ac), the denominator of it is 2a. The numerator of the other fraction is -b, the denominator of it is 2a as well. They have the same denominator, and thus they can combine. Plus minus is two operations, addition and subtraction.
If you're talking about plus-minus in the denominator, well here's the thing. If the denominator is negative and the numerator is positive, the whole fraction is negative. If the denominator is negative and the numerator is negative, the whole fraction is positive. If the denominator is positive and the numerator is positive, the whole fraction is positive. If the denominator is positive and the numerator is negative, the whole fraction is negative.
I used to solve quadratic equations, now I know how it came from.
Solving is one thing, understanding it is euphoric, thanks Sir
Starting with a pickup line, "formulas have a ...." making jokes, having fun, this guy made a math class seem like English, so darn easy and fun! I can't believe these kind of teachers existed in past..
Fantastic. In my school, high school and college, they just give the quadratic formula but you derived it. You showed how it arrived to that formula.
is it my computer or is the audio on this video is fucked up, i almost scream.
its the video. he was trying a different mic for this video
I remember reading this from the Math book in 8th grade and it was great to see the original equation becoming the formula that the teacher told us to use without knowing why. I must be the only kid who cared to know back then
And congrats to the Professor
Mr. Woo, you are an incredible instructor.
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
OMG that's so interesting! Wish I had you as my maths teacher
0:28 Interestingly, before the digital age and the advent of ELECTRONIC computers, PEOPLE who did computations were computers.
I used to always tell my friends that computer used to be a job and not a device. lol
My boy must be dropping a lot of n words in this video lol
60 years ago during my mathematics GCE 'O' level I derived the formula on scrap paper because I could not remember the formula but I did understand where it came from.
are you in freshman year? Iam in 5th grade
@@frenchfatfather9308 second childhood!
The quadratic formula has been one of my favorite formulas and I never understood how it related to a quadratic equation. None of my math teachers ever took the time to show WHY it works, just told us to use it because it worked.
Hi Eddie, this is a "pre-viewing comment", I'm about to show this video to my very bright Year 9 class. One of your videos really helped me with Logs, so I'm giving you the chance with my Year 9 🙂
It might be the video's age, but the sound goes out at random times. I tried showing this to my class last week, but the sound breaks proved to be a large distraction for them. Great video otherwise
my teachers never swore so much!!
You are the best teacher of the world sir
Well, not only did my class love the video, it's really strengthened my knowledge of this topic. I've subscribed, I hope you are looking into getting monetised, us teachers deserve every penny we get! I think some of my class have subscribed to you.
What’s up with sound
A minor point. Radical 4a^2 is not necessarily 2a. It could be -2a if a is negative. It doesn't affect the final solution, but we shouldn't ignore this issue.
In this case it is, because he got the 4a^2 from squaring 2a itself. So it becomes sqrt((2a)^2)=2a
i know this is a few years late but ill share this anyway,
that is actually a common misconception!
the plus and minus only applies to:
x^2 = 4
x = ± √4
x = ± 2
but in radicals, √(a^2) = |a|
so √4 is always just 2 (called the principal root), even if √4 can be written as √ [(-2)^2], it is equal to |-2|, thus it's still just 2. It can only become -2 if it is indicated with a negative sign outside the radical, i.e. -√4. Hope this was helpful! xx
This is great and so straight-forward!!! I wish my high school had taught this!!!!!
In india this quadratic formula is named as shri dharacharya formula. Given by indian mathematician dharacharya ji.
Funny, but I learned this quadratic derivation at high school at 15 years old, and I’m 53 now, and never forgotten this formula!
Drinking challenge: take a shot every time the audio cuts off.
Great to know how that formula evolved....thankyou
Y dont we have maths teachers like u in our school !!! Thank u so much for this. I always had a trouble with d quadratic formula !
Best quality of sound.
i still dont get the step at 4:20...why do we divide it by 2 and then square it? What is the purpose of doing that and is there a rule telling us to do that? I dont remember ever having to divide anything by 2 and squaring it in all my math experience
Say you had x^2-2x on the LHS. What you always have to do when you have something like this is to half the coefficient of x, then square it to get x^2-2x+((1/2)×(2))^2 = x^2-2x+1
= (x-1)^2.
It's because the middle term is always twice the (square root of) other terms multiplied, e.g.
x^2+6x+9 (9 =3^2) =
(1)x^2+2(1x)(3)+3^2
(ax+b)^2 = a^2x^2+2abx+b^2
Can someone explain to be why b squared under the root doesn’t become b outside the root?
Because there isn't another b^2 in the second half of the term under the square root. There is no b^2 in the term -4*a*c.
You cannot factor sqrt(x^2 - y) as x*sqrt(1 - y), so you cannot do the same with sqrt(b^2 - 4*a*c).
In the special case that c=0, then the b^2 does do exactly what you are asking for. One might also think that a could equal zero for the same thing to happen, and they would be somewhat correct. But if a=0, then the entire denominator would equal zero, which cannot be. We'd also not even have a quadratic, as we'd have a line.
Brilliant. Thanks!
Which year of students do you teach this topic?
omg, u always just the best teacher ever!! ❤️❤️🤸
BUT THE Square Root of 4a^2 CAN BE -2a that is negative 2a?
this formula is given by श्री धराचाय(श्री धर आचार्य) an Indian mathamatician❤❤
Would someone explain why he have to say + or - the a when he takes square root of the a^2 at the end!? He said plus or minus for the big part that he takes square root of, but when he gets to square rooting the a^2 at the end, he doesn't do another + or - !
I just had my mind blown
that is so cool
I've been desperately looking for an explanation of WHY the quadratic equation works for YEARS but your mic keeps cutting out :(
best i've seen , thanks; audio cuts out a bit tho..
audio seems broken
I have a question. In 8:51, wouldn't it be square root of 4a^2 is positive or negative 2a? Cause we always consider negative when looking for square root right?
true but in each case of a the overall fraction would still be positive or negative so it won't really matter
@@lafyouthclub281 can you explain a bit more about this?
Yes! You are right. This is a quibble I have with all the derivations of the quadratic formula. They all ignore this point. At the end it doesn't matter +radical(b^2-4ac)/(-2a) = -radical(b^2-4ac)/2a. And -radical(b^2-4ac)/(-2a) = +radical(b^2-4ac)/(2a). So at the end we still get +-radical(b^2-4ac)/(2a). The order just gets changed, but we don't care about the order.
But a way to clean this up is by to first multiply both sides by 4a^2 before taking square roots.
4a^2(x+b/(2a))^2 = b^2-4ac
(2a(x+b/(2a))^2 = b^2-4ac
Now we can take square root and avoid this issue:
2a(x+b/(2a)) = +-radical(b^2-4ac)
etc... Now the issue of the sign of a doesn't matter.
The sound keeps dropping out on this video. You might want to redownload it.
The sound comes in broken at times, can't hear the lecture completely.
Thank you... got a lot of information.
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
Sound is broken up at the beginning.
Grade 11, and im just finding out where this formula comes out from
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
can you repeat it? The most important info got cut off. I don't understand what's going on. Why b/2a?
qiankun danuoyi, it comes from the process of completing the square. See this video where Eddie explains this process geometrically. He starts explaining the "b/2a" part at 1:10.
czcams.com/video/McDdEw_Fb5E/video.html
It’s of consequence of completing the square. Once that’s done, the 2 and a in the two denominators of the left side combine(are multiplied)
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
MAGIC!
Fact: this formula was made by India's Sri dharacharaya.
Amazing Sir
what with sound?
Good work. {a,b,c are any numbres and a ≠ 0}.
CalculoTV well yeah because then the denominator would be 0
It will be a linear expression then
You can have perfect square trinomials where 'A' isn't one; For example; 9(x^2)-24x+16, is a perfect square. Why did you say that?
yes when you factorise a quadratic you can have that, however when you are solving one you can just divide the whole quadratic by a and divide 0 by a to make it easier and it will still work
Issue with the audio
Were you abusing when the sound wasn't coming
Why is it b/2a instead of just b/a ??
Leo Callebaut, b/2a comes from the process of completing the square. See this video where Eddie explains this process geometrically. He starts explaining the "b/2a" part at 1:10.
czcams.com/video/McDdEw_Fb5E/video.html
@@Tekkerue Thanks for this, completing the square was a concept that I never revisited. It all makes sense now!
@@Isomnophilia You're welcome. :) Visual explanations like that really help to intuitively understand what you are doing and why as opposed to just memorizing formulas. I never got that kind of intuitive explanation in school, but is great that there are so many amazing lessons available now on the internet.
@@Tekkerue this is the future of teaching. Subscribing to qualified teachers for quality material. Conferencing / VR / instant referencing... resources are there to create virtual schools eventually.
@@Isomnophilia Yeah, there are already college courses available online from universities like Stanford, Harvard, MIT, etc where you can watch full videos of the course lectures and some of the courses even have homework assignments too so you get the whole course for free. Pretty cool! :) Then there are amazing CZcams channels who are not accredited teachers, but they do an amazing job teaching the material, like 3Blue1Brown who is seriously in a league of his own. It's only a matter of time before that "piece of paper" becomes essentially worthless because people can get a better education through resources online rather than sitting in a classroom with a crap teacher who can't teach the material even half as well. lol
Now this is a teacher
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
Anyone know what grade he teaches
Mainly Year 10, 11 and 12 on wootube, but also junior high school (Year 7 and 8). I'm guessing this is Year 10 content in Australia.
i LOVE maths!
But a is not equal to zero
If a were equal to zero, you wouldn't even have a quadratic equation in the first place; you'd have a linear equation, and you wouldn't need to even think about this formula.
What's wrong with audio
In what grade is this ?
Heavily censored video
hello sir
iam saksham from india
my base is weak and I am in grade 10 please help for making my base strong
i love u
didn't know numbers will be censored :))
@@koketsobaholo7 r u ok?
Does your school has igcse curriculum?
Good news!!!!!!!!!
Therefore repent and turn back, so that your sins may be wiped out, that seasons of refreshing may come from the presence of the Lord, and that he may send Jesus, who has been appointed for you as the Messiah.
Acts 3:19?-?20 CSB
From then on Jesus began to preach, “Repent, because the kingdom of heaven has come near.”
Matthew 4:17 CSB
“The time is fulfilled, and the kingdom of God has come near. Repent and believe the good news!”
Mark 1:15 CSB
Jesus replied, “Truly I tell you, unless someone is born again, he cannot see the kingdom of God.” Jesus answered, “Truly I tell you, unless someone is born of water and the Spirit, he cannot enter the kingdom of God.
John 3:3?, ?5 CSB
Whoever claims to live in him must live as Jesus did.
1 John 2:6 NIV
1john.bible/1-john-2-6
Jesus told him, “I am the way, the truth, and the life. No one comes to the Father except through me.
John 14:6 CSB
For God loved the world so much that he gave his only Son, so that everyone who believes in him may not die but have eternal life.
John 3:16 GNB
bible.com/bible/296/jhn.3.16.GNB
_Jesus_ actually died, *_GOD_* has _His blood_ as a sacrifice for your sins. *_GOD_* killed *_His_*_ Only Son_ for you. All your sins: sexual immorality (fornication, adultery(lust), homosexual sex, pornography) murder( hating someone, envying, abortion and killing someone) , theft( murder, lying, abuse, corruption, disrespect, racism) and idolatry (greed, love of money, worship of other gods and pride) can be forgiven only if you believe in _Jesus_; that __*_God_* sacrificed _Him_ for the atonement of all your sins, and that_*He*_ raised _Him_ up 3 days later. And now He sits on the Right Hand of *_The Father_*__, ruling over all creation as __*_Lord and Saviour_* of the world.
Jesus Christ died for your sins, and only through Him you can be forgiven of all your sins.
You only go to heaven because of faith and belief in The death and resurrection of _The Son of _*_God_* for the sins of the world.
Hell is for those reject GOD'S Only Son, they will be burnt by the wrath of The Almighty God.
Believe that all your sins are forgiven because of The Blood of Jesus, who is The Messiah, The Saviour.
Repent, turn away from your sins and live because,
*_Jesus Lives_*
Im starting to think theres no difference between mathematics and magic
Error inside the square root: 4ac = 4(1)(-3) = -12 which implies 1 - (-12) = 1 + 12 = 13. 🌿
technically, a has to be nonzero
Well, I get what you mean, but this is a formula for quadratic equations, and if a is equal to zero, you have a linear equation instead.
@@koketsobaholo7 what has this to do with this comment?
I think the coefficient a can't be any number, because if it were a zero, you would have a linear equation and not a quadratic.
It's the third time I've been seen a video from Mr. Who about Quadratic formula derivation and I still pull out my hair when he straightforward takes the square root of the second member before even assuming b²-4ac is non negative... Actually the formula is correct if and and only if b²-4ac is non negative. And magically (luck or wellc chosen examples) all the examples he gives are Delta positive. This is really important to notice the case Delta < 0 because it might be tricky when students will face a non positive delta...
Eddie does talk about cases with delta < 0 later on, which is recorded on other videos. There is no need to talk about everything at once, it's better to teach stuff gradually.
Besides, the formula is always correct, even if the discriminant is negative, you just have to look outside of real numbers.
@@vooyeq1730 No it is not, as the formula in this case would be +/_( i sqrt(|b^2 - 4ac|) /2a. This is not semblable
One has to be rigorous about it
You can get the newer version of the quadratic formula here. :)
czcams.com/video/38TysPMjU7E/video.html
By Eddie woo
You made a mistake when you were substituting the numbers into your formula where -b isnt 1 its -1 because its -(b) or -(1)
If you look closely, there's already a - before the b so it's technically -(-1) = 1 so he was correct
it doesn't work like that the sign on 1 is counted when using the quadratic formula
You really often use the f word!
Never fully got this in 1992. Now I finally understand it🥹 And yes, better math teachers slow down and explain each step because it’s a lot of steps. Perfect!