# What is the vertex form of y=x^2 + 4x + 2?

Nov 16, 2015

$y = {\left(x - \left(- 2\right)\right)}^{2} + \left(- 2\right)$

#### Explanation:

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

$y = {x}^{2} + 4 x + 2$

Complete the square:
$\textcolor{w h i t e}{\text{XXX}} = {x}^{2} + 4 x + 4 - 2$

$\textcolor{w h i t e}{\text{XXX}} = {\left(x + 2\right)}^{2} - 2$

Adjust signs to get vertex form:
$\textcolor{w h i t e}{\text{XXX}} = {\left(x - \left(- 2\right)\right)}^{2} + \left(- 2\right)$
with vertex at $\left(- 2 , - 2\right)$