# What is the vertex form of  4y = x(x+12)+13 ?

Dec 25, 2015

$y = \frac{1}{4} {\left(x - \left(- 6\right)\right)}^{2} + \left(- 6\right)$
$\textcolor{w h i t e}{\text{XXXXXXXXXXX}}$with vertex at $\left(- 6 , - 6\right)$

#### Explanation:

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

Given:
$\textcolor{w h i t e}{\text{XXX}} 4 y = x \left(x + 12\right) + 13$
Expand the right side
$\textcolor{w h i t e}{\text{XXX}} 4 y = {x}^{2} + 12 x + 13$
Complete the square
$\textcolor{w h i t e}{\text{XXX}} 4 y = {x}^{2} + 12 x \textcolor{g r e e n}{+ {6}^{2}} + 13 \textcolor{g r e e n}{- 36}$
Rewrite as a squared binomial (and combine the constant)
$\textcolor{w h i t e}{\text{XXX}} 4 y = {\left(x + 6\right)}^{2} - 24$
Divide both sides by $4$
$\textcolor{w h i t e}{\text{XXX}} y = \frac{1}{4} {\left(x - \left(- 6\right)\right)}^{2} + \left(- 6\right)$