# How do you write y = 2x^2-12x+11 into vertex form?

May 29, 2015

The general vertex form for a quadratic is
$y = m \left(x - a\right) + b$ where $\left(a , b\right)$ is the vertex.

$y = 2 {x}^{2} - 12 x + 11$
$\textcolor{w h i t e}{\text{XXXX}}$extract the $m$
$y = 2 \left({x}^{2} - 6 x\right) + 11$
$\textcolor{w h i t e}{\text{XXXX}}$complete the square
$y = 2 \left({x}^{2} - 6 x + 9\right) + 11 - 18$
$\textcolor{w h i t e}{\text{XXXX}}$simplify to vertex form
$y = 2 {\left(x - 3\right)}^{2} + \left(- 7\right)$
$\textcolor{w h i t e}{\text{XXXX}}$with the vertex at $\left(3 , - 7\right)$