vertex form of a quadratic equation (proof of formula!)

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In this video I prove the formula for the vertex form of a quadratic equation. I show how the standard form of a quadratic equation, along with the formula for the vertex of a quadratic equation can be used to derive the vertex form of a quadratic equation formula.

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Комментарии
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This might be the greatest math video I have ever seen

realsm
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Excellent video! I remember seeing this formula in school, but I never quite understood where it came from. You explained it beautifully.

The only thing some people might get a bit confused with is why h = -b/2a. The way I understand that one is to take the first derivative of a generic quadratic equation ax²+bx+c, which becomes 2ax+b. The slope of the quadratic is 0 at its vertex point, so 0 = 2ax+b, which you can solve for x to get x = -b/2a. Hopefully this comment might help someone to understand this a bit better, although it does require an understanding of derivatives which normally comes after studying this part of functions.

FootballPsychoPST
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This is beautiful. Is it just luck that we get a perfect square trinomial at the end? I want to see how they found this in the first place. Gorgeous equation

Nick_Reinhardt