But where does the quadratic formula come from?

In this video we explore how to derive the quadratic formula visually, and learn some insights about how to visualise equations along the way.

[@KarlHeinzSpock]

i already knew the algebraic derivation of the formula, but the combination between formula and corresponding geometric shape is really well done!

[@makermaker11]

Dude we need more people like you people just shove equations in our mind without telling us how they work😂

[@stevenlitvintchouk3131]

The method of solving quadratics by completing the square was first discovered by an Islamic mathematician, Al-Khwarizmi, in the 9th century A.D. Completing the square is still taught to schoolchildren today.

[@ranjanasingh3557]

It's shridharacharya's rule

[@mianmauzgujjar8528]

@@ranjanasingh3557 bullshit

[@makermaker11]

Bullshit​@@ranjanasingh3557

[@MyYoutube-my3ok]

سلطان خوارزمی

[@Vayu_arya]

​@@mianmauzgujjar8528it's true it's sridharacharya rule your Arabs learnt mathematics from india your Arabs cam eto india not indians went to arab

[@DDXMalow]

I’ve seen lots of videos explaining this, this is the best one, great explanations and great visuals🎉

[@foggymaths]

Thank you so much!

[@StackzBetter]

This video saved me.... On a MAP test (adaptive test) I took yesterday (8th grade), I got up to the point which asked me to get from the quadratic equation to the quadratic formula... Couldn't have done it without this video ❤! Ty for this video!

[@AchtungBaby77]

When I first learnt the quadratic formula in school, it was introduced graphically which I found far more intuitive than completing the square.
For a general quadratic ax² + bx + c = 0, we know that the vertex is located at x= -b/2a, so you simply replace x by (x - b/2a) to "shift" the parabola to the y-axis.
This gives you a super simple quadratic to solve of the form x² + A = 0, which you can trivially solve, then you simply "undo" the shift by adding in the -b/2a term again.

[@user-ex5cw8ox2r]

thanks a lot for giving the actual derivation of the formula with geometry

[@justinlloyd625]

Great video! Very clear, informative, and insightful!

[@smokeman2645]

in your recording apply a low-pass filter so your (high frequency) lip/spit/tongue sounds are less noticable (or mix it better). In normal conversation we dont hear that but when you record your voice the mic pics up a lot more as its up close.
good luck!

[@foggymaths]

Thank you, I’ve tried to improve this in later videos ^^

[@MScienceCat2851]

Oh my god. This is absolutely brilliant!

[@wirayudhabn]

Fantastic

[@nikthedrought]

love u bro

[@amitchakrabortty3357]

Need more vedeo

[@rururu5877]

Isnt sqrt(x²)=abs(x)? As if you took the square root like that what you get in the end is inly the positive solution?

[@foggymaths]

Yes, hence the ± syntax.

[@anonyone8834]

Good video

[@ayushraj9e156]

This Formulae was given by the Indain mathematician "Shridharacharya"

[@harpoon2445]

At 2:39, the plus/minus sign came in too early. Only when the square on the lhs is offset against the square root do you get the plus/minus on the rhs.

[@erikyahirvillamilsanchez2156]

Underated video !

[@NinjaMelon21]

Damn good explanation ❤️

[@DiscoCubes64]

Really good!

[@stevejones6330]

Killer demo.

[@SolathPrime]

I was in middle school when I took this path to find it
at secondary school I took the calculus path to it

[@wtz_under]

geez. im fortunate not to take A Math. A Math is where caluculus is taught

[@mendozajovy]

Completing the square AX^2+BX+C=0. Isolate X.

[@bidam224]

I satisfied man. thanks a lot

[@boi8068]

Thank you

[@maliketh1173]

these look like vertasium type visuals

[@odysseasv7734]

i think you mean 3blue1brown

[@GlortMusic]

@@odysseasv7734 Yes, you can make animations like the ones in this video with 3b1b's library (Manim).

[@wtz_under]

fr. im surprised this isnt reccomended

[@biophonism]

Why does the +- sign appear at 2:38?

[@henricobarbosa7634]

Because he is solving for x^2 = c (c is just a positive number). When taking the square root in both sides you need to take the negative value into account as well. Here both sqrt(c) and -sqrt(c) when squared will be equal to c

[@shinobi6497]

At 2:42 how does the 4a^2 shift to 2a and stop being square rooted

[@bilaalahmed8923]

Because √(ab) = √a × √b. So the √4a² is √4 * √a² the square root of 4 is 2 and square root of a² is a so its 2a

[@maxjoe7107]

2:45

[@pandurangaraonimmagadda9966]

a xsquare+b x+c=0 is the quadratic equation

[@morpheus6408]

School doesn’t want that their students understand, they just want that we memorizing

[@fullmindstorm]

Welp. After this excellent visual explanation and understanding, now I think the quadratic formula is useful but how much it takes to get to the quadratic formula is gae. 😭

[@oraach]

Neaaaaat

[@SaagarNayak]

The thumbnail is wrong, the negative sign is not on the outside, its on the inside

[@elliotlambert3817]

The formulae is written incorrectly -b is correct not all the formulae -

[@ChavoMysterio]

Simple. Completing the square from ax^2+bx+c=0 would prove the quadratic formula.

[@humbledb4jesus]

algebra, silly

[@Nikioko]

The quadratic formula: x₁,₂ = - p/2 ± √[(p/2)² - q]
A lot easier than the monster in this video.

[@bradleywang289]

that’s the same thing, just without a x^2 coefficient

[@waaahhhvishhh9408]

Bruh u fool

[@d.bpatil6361]

The solution given is wrong. The minus sign is only for 'b' and not for whole.

[@foggymaths]

Putting the minus sign in front of the fraction or on the b makes no difference to the formula, effectively putting it out front multiplies the top through by -1, the b becomes -b, the ‘+/-‘ is still ‘+/-‘

[@wtz_under]

@@foggymathsits a little confusing though. you could give us both ways of writing the equation done