# What is the vertex form of y= x^2+9x-22 ?

Dec 24, 2015

$y = {\left(x - \left(- \frac{9}{2}\right)\right)}^{2} + \left(- \frac{169}{4}\right)$

#### Explanation:

General vertex form:
$\textcolor{w h i t e}{\text{XXX}} y = {\left(x - a\right)}^{2} + b$ with vertex at $\left(a , b\right)$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 9 x - 22$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = {x}^{2} + 9 x \textcolor{red}{+ {\left(\frac{9}{2}\right)}^{2}} - 22 \textcolor{red}{- {\left(\frac{9}{2}\right)}^{2}}$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = {\left(x + \frac{9}{2}\right)}^{2} - 22 - \frac{81}{4}$

$\rightarrow \textcolor{w h i t e}{\text{XXX}} y = {\left(x - \left(- \frac{9}{2}\right)\right)}^{2} + \left(- \frac{169}{4}\right)$

which is the vertex form with vertex at $\left(- \frac{9}{2} , - \frac{169}{4}\right)$