# How do you find the vertex of a quadratic equation y= -x^2 + 9?

Jun 9, 2016

Vertex at: $\left(0 , 9\right)$

#### Explanation:

The general explicit vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
for a parabola with vertex at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

The given equation: $y = - {x}^{2} + 9$
can be converted into the explicit vertex form as
$\textcolor{w h i t e}{\text{XXX")y=color(green)(} \left(- 1\right)} {\left(x - \textcolor{red}{0}\right)}^{2} + \textcolor{b l u e}{9}$
for a parabola with vertex at $\left(\textcolor{red}{0} , \textcolor{b l u e}{9}\right)$

For verification purposes, here is the graph of the original equation:
graph{-x^2+9 [-12.96, 12.35, -2.49, 10.17]}