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2akondupa

Answered question

2022-03-17

Can't solve quadratic function
I'm trying to get a simple quadratic function of the form

y = a x^{2} + b x + c

which goes through the following points:

(0; 0); (\frac{d}{2}; 2); (d; 0)

varkdrafx9w

Beginner2022-03-18Added 4 answers

The key bit to notice is that you've been given the roots of such a quadratic. Namely the roots are

x = 0 and x = d

. This must mean your quadratic can be written of the form

{y = A x (x - d)}

(since any polynomial can be factorised over it's roots) where A is a constant to be determined.
If we plug in

x = \frac{d}{2}

, want the result to be 2. As an equation, that is

{A \frac{d}{2} (\frac{d}{2} - d) = 2}

We can then rearrange for A to get

{A = \frac{2}{\frac{d}{2} (\frac{d}{2} - d)} = \frac{- 8}{d^{2}}}

Hence

{y = \frac{- 8}{d^{2}} x (x - d) = - \frac{8}{d^{2}} x^{2} + \frac{8}{d}}

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