# How do I use the vertex formula to determine the vertex of the graph for y = x^2 - x + 2?

Apr 30, 2015

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

We want to convert this into the form
$y = m {\left(x - a\right)}^{2} + b$

Since the coefficient of ${x}^{2}$ in the given form is $1$
$m = 1$
and the problem is a "complete the squares" problem

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

$y = {\left(x - \frac{1}{2}\right)}^{2} + 1 \frac{3}{4}$

and the vertex is at $\left(- \frac{1}{2} , 1 \frac{3}{4}\right)$