# What is the vertex form of y=x^2+9x+3 ?

Apr 21, 2018

$\left(- \textcolor{red}{\frac{9}{2}} | \textcolor{g r e e n}{- \frac{69}{4}}\right)$

#### Explanation:

$y = {x}^{2} + 9 x + 3$
$y = {x}^{2} + 2 \cdot \frac{9}{2} x + {\left(\frac{9}{2}\right)}^{2} - {\left(\frac{9}{2}\right)}^{2} + 3$
$y = {\left(x + \frac{9}{2}\right)}^{2} - \frac{81}{4} + 3$
$y = {\left(x + \textcolor{red}{\frac{9}{2}}\right)}^{2} \textcolor{g r e e n}{- \frac{69}{4}}$

The vertex is at $\left(- \textcolor{red}{\frac{9}{2}} | \textcolor{g r e e n}{- \frac{69}{4}}\right)$