# How do you write y= 2x^2 - 8x + 13 into vertex form?

May 22, 2015

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

Given $y = 2 {x}^{2} - 8 x + 13$

Extract $m$

$y = 2 \left({x}^{2} - 4 x\right) + 13$

Complete the square

$y = 2 \left({x}^{2} - 4 x + 4\right) + 13 + 8$

Complete writing in vertex form

$y = 2 {\left(x - 2\right)}^{2} + 21$