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!

[makermaker]

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

[ponyonoodles]

In maths the other day I asked why, when translating f(x), the vector (a 0) is found by f(x-a) and not f(x+a). The other students in my class tried explaining, but they didn't understand that I knew how to solve it exercises, just not _why_ it was that way. The maths teacher understood me, but she couldn't explain it. Finding out why was my homework this weekend. This was such a simple and short way to explain it, I'm going to use this explanation during my next maths class hehe. Tysm!!

[stevenlitvintchouk]

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.

[DDXMalow]

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

[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!

[AchtungBaby]

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.

[zeus-zd]

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

[ayushraje]

This Formulae was given by the Indain mathematician "Shridharacharya"

[smokeman]

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!

[rururu]

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?

[justinlloyd]

Great video! Very clear, informative, and insightful!

[MScienceCat]

Oh my god. This is absolutely brilliant!

[harpoon]

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.

[maliketh]

these look like vertasium type visuals

[SolathPrime]

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

[mendozajovy]

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

[shinobi]

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

[morpheus]

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

[SaagarNayak]

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