# What is the the vertex of y = x^2-6x+6?

Jun 11, 2016

vertex: $\left(3 , - 3\right)$

#### Explanation:

The general vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
for a parabola with vertex at $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$

Given
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 6 x + 6$
$\Rightarrow$
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - \textcolor{c y a n}{6} x \textcolor{\mathmr{and} a n \ge}{+} {\left(\frac{\textcolor{c y a n}{6}}{2}\right)}^{2} + 6 \textcolor{\mathmr{and} a n \ge}{-} {\left(\frac{\textcolor{c y a n}{6}}{2}\right)}^{2}$

$\textcolor{w h i t e}{\text{XXX")y=(x-color(red)(3))^2+color(blue)(} \left(- 3\right)}$

which is the vertex form with vertex at $\left(\textcolor{red}{3} , \textcolor{b l u e}{- 3}\right)$

For verification purposes, here is a graph of the original equation:
graph{x^2-6x+6 [-3.506, 7.595, -3.773, 1.774]}