# How do you write the quadratic function in vertex form given vertex (-6,-7) and point (0,-61)?

Aug 15, 2017

$y = - \frac{3}{2} {\left(x + 6\right)}^{2} - 7$

#### 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.

$\text{here } \left(h , k\right) = \left(- 6 , - 7\right)$

$\Rightarrow y = a {\left(x + 6\right)}^{2} - 7$

$\text{to find a substitute "(0,-61)" into the equation}$

$- 61 = 36 a - 7 \Rightarrow a = - \frac{3}{2}$

$y = - \frac{3}{2} {\left(x + 6\right)}^{2} - 7 \leftarrow \textcolor{red}{\text{ in vertex form}}$