# How do you write 4x^2-4x+2 in vertex form?

May 21, 2015

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

The general vertex form is
$y = m {\left(x - a\right)}^{2} + b$ where $\left(a , b\right)$ is the vertex of the parabola

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

Complete the square
$y = 4 \left({x}^{2} - x + \frac{1}{4}\right) + 2 + 1$

Rewrite in vertex form
$y = 4 \left(x - \frac{1}{2}\right) + 3$