# What is the vertex of  y= x^2-2x+8?

Feb 16, 2016

vertex: (x,y)=1,7)

#### Explanation:

The easiest way to find the vertex is to convert the given equation into "vertex form":
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{m} {\left(x - \textcolor{red}{a}\right)}^{2} + \textcolor{b l u e}{b}$
with a vertex at (color(red)(a),color(blue)(b))

Given
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 2 x + 8$

Complete the square:
$\textcolor{w h i t e}{\text{XXX}} y = {x}^{2} - 2 x + 1 + 7$

$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{g r e e n}{1} {\left(x - \textcolor{red}{1}\right)}^{2} + \textcolor{b l u e}{7}$
which is in "vertex-form".

graph{x^2-2x+8 [-3.684, 8.8, 5.06, 11.3]}