-b/2a = x value of turning point = -(10)/2(1) = -5 Plug -5 back into the quadratic to find y value f(-5) = (-5)^2+10(-5)+24 = -1 Turning Point = (-5,-1)
Bro thanks.. here is an easy way of doing it a=1 b=10 c=24 Step 1. p= -b/2a p=-(10)/2(a) p=-10/2 p=-5 Note: p is equals to the x coordinate . Step 2: q= 4(a) (c) - (b)²/ 4(a) q=4(1) (24) - (10)²/ 4(1) q= 96 - 100/ 4 q=-4/4 q= -1 (-5,-1) Note: q is equals to the y coordinate.
when we have a quadratic eqn with a negative coefficeint, does this still work as is or must we take the - sign in common and THEN carry the formula out?
A quadratic only has one turning point but for equations with two turning points you can use calculus. If the derivative = 0 and the second derivative does not = 0 then it is a turning point. If you find all the x values that make the first derivative 0, you can test them by plugging in to the second derivative to make sure the second derivative does not = 0. You can then plug in all the x values that passed the test into the original function to get the y coordinates of the turning points. I also think it is easier to use derivatives for quadratic functions to find turning points. You can super easily find the derivative in your head which would be 2x + 10. If you set it equal to 0, you get that the x coordinate is -5 and you plug that back in to the original function to get the y coordinate. You don't need to check the second derivative because there are no points of inflection on a quadratic.
When you change x² + 10x into (x + 5)², the x² and the 10x remain the same, but you end up with an additional product of 25, which must be negated by subtracting 25.
basically what he did was +(5)^2 which went in the bracket with x making it (x+5)^2 then -(5)^2 which gave us -25. If u want to know the reason behind this, he used the completing square method. I recommend watching a few videos on it as it is really easy to learn and helps a lot with problems like these and is the easiest method to figuring out equations of circles.
Here is something for you a=1 b=10 c=24 Step 1. p= -b/2a p=-(10)/2(a) p=-10/2 p=-5 Note: p is equals to the x coordinate . Step 2: q= 4(a) (c) - (b)²/ 4(a) q=4(1) (24) - (10)²/ 4(1) q= 96 - 100/ 4 q=-4/4 q= -1 (-5,-1) Note: q is equals to the y coordinate.
Homie you literally saved me a shit ton of time, even chatgpt couldnt do it for me lol. Thanks alot bro appreciate u
My pleasure mate, glad it helped 🙏🏻
it actually can if you ask for the specific X and Y
-b/2a = x value of turning point
= -(10)/2(1) = -5
Plug -5 back into the quadratic to find y value
f(-5) = (-5)^2+10(-5)+24
= -1
Turning Point = (-5,-1)
Bro you are actually so underrated thank you so much
My pleasure mate 🙏🏼 Blow up coming this year hopefully 🚀
OMG GOD BLESS YOU OMGGGG I WASN'T UNDERSTANDING ANYTHING YOU SAVED ME THANK YOU THANK YOU 🩷🩷🩷🩷
Soooo glad it helped! 🙌⚡️
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@@kleesbombs YES
Bro thanks.. here is an easy way of doing it
a=1
b=10
c=24
Step 1.
p= -b/2a
p=-(10)/2(a)
p=-10/2
p=-5
Note: p is equals to the x coordinate .
Step 2:
q= 4(a) (c) - (b)²/ 4(a)
q=4(1) (24) - (10)²/ 4(1)
q= 96 - 100/ 4
q=-4/4
q= -1
(-5,-1)
Note: q is equals to the y coordinate.
Another way is using -b/2a = x or just turning the equation into the standard form and solving it
Do -b/2a and plug the answer into the quadratic to get your y value and use the same x value
Amazing 🥰 I'll understand, answer and pass my exams with flying colours in the same way Amen🙏
Thanks so much, first day of geometry and reviewed from last year. Didn’t get any of it and now I do in 2 mins of trying thx so much.
Great to hear! So glad it helped 🤩
I have my baseline test for gcse recap tomorrow and I'm in yr12 I forgot about this and you saved me time and is very useful
Thank you
Mine's today and this really is a help to me
thank you
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Thank you for the helpful video
My pleasure! ⚡️
thanks for saving time\
My pleasure! Thanks for the comment ⚡️
God bless you
Bro you're smart.
If the x was a number would u also divide the number by 2? Pls someone tell me I have my maths test tomorrow
0:30 ohh
What about if the C term after completing the square is a positive?! For example (x+3)²+9
Cheers
I love you
when we have a quadratic eqn with a negative coefficeint, does this still work as is or must we take the - sign in common and THEN carry the formula out?
🥰🥰🥰 the tutor😅
what if the coefficient is an odd no. ?
Same idea you would halve the odd number so you would just half it.
Wow
Why does he half x^2 and 10x? Just a step that confuses me a bit🙏🏼
❤❤❤
Too much stuff I gotta learn might as well just flip burgers but cheers mate
hi what to do if there are two turning points will this trick work in that
No it won’t, but you don’t have to worry about any graphs with two turning points in GCSE Maths
A quadratic only has one turning point but for equations with two turning points you can use calculus. If the derivative = 0 and the second derivative does not = 0 then it is a turning point. If you find all the x values that make the first derivative 0, you can test them by plugging in to the second derivative to make sure the second derivative does not = 0. You can then plug in all the x values that passed the test into the original function to get the y coordinates of the turning points.
I also think it is easier to use derivatives for quadratic functions to find turning points. You can super easily find the derivative in your head which would be 2x + 10. If you set it equal to 0, you get that the x coordinate is -5 and you plug that back in to the original function to get the y coordinate. You don't need to check the second derivative because there are no points of inflection on a quadratic.
❤
Why do you subtract 25
wait but how do you plot the graph
Isnt dy/dx easier… (help im going insane over this.. quadratic graph😭)
You could also find dy/dx, set it equal to zero, solve for x, and sub in to find y
never have i understood math so quickly, thank yo broski 🫶
👍
Diffrentiate and equate the function to zero ez
Why did the (x+5)² become -25?
When you change x² + 10x into (x + 5)², the x² and the 10x remain the same, but you end up with an additional product of 25, which must be negated by subtracting 25.
search how to complete square method on youtube
basically what he did was +(5)^2 which went in the bracket with x making it (x+5)^2 then -(5)^2 which gave us -25. If u want to know the reason behind this, he used the completing square method. I recommend watching a few videos on it as it is really easy to learn and helps a lot with problems like these and is the easiest method to figuring out equations of circles.
Here is something for you
a=1
b=10
c=24
Step 1.
p= -b/2a
p=-(10)/2(a)
p=-10/2
p=-5
Note: p is equals to the x coordinate .
Step 2:
q= 4(a) (c) - (b)²/ 4(a)
q=4(1) (24) - (10)²/ 4(1)
q= 96 - 100/ 4
q=-4/4
q= -1
(-5,-1)
Note: q is equals to the y coordinate.