# How do you write the quadratic function in vertex form given vertex (0,0) and point (-2,-12)?

##### 1 Answer
May 25, 2017

$y = - 3 {x}^{2}$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where ( h , k ) are the coordinates of the vertex and a is a constant.

$\text{here } \left(h , k\right) = \left(0 , 0\right)$

$\Rightarrow y = a {x}^{2}$

$\text{to find a, substitute " (-2,-12)" into the equation}$

$- 12 = 4 a \Rightarrow a = - 3$

$\Rightarrow y = - 3 {\left(x - 0\right)}^{2} + 0 \leftarrow \textcolor{red}{\text{ in vertex form}}$