How do you write a quadratic function in vertex form whose graph has the vertex (0,0) and point (2,4)?

Mar 25, 2017

The vertex form of a quadratic function is:

$y = a {\left(x - h\right)}^{2} + k$

Explanation:

Given the vertex is at $\left(0 , 0\right)$, then $h = 0$ and $k = 0$:

$y = a {\left(x - 0\right)}^{2} + 0$

You can find the value of "a" using the point $\left(2 , 4\right)$

$4 = a {\left(2 - 0\right)}^{2} + 0$

$4 = 4 a$

$a = 1$

The vertex form of the function is:

$y = 1 {\left(x - 0\right)}^{2} + 0$

This simplifies to:

$y = {x}^{2}$