# How do you find the vertex of a parabola y = x^2 - 6x + 10?

Jun 30, 2015

The vertex is at $\left(3 , 1\right)$

#### Explanation:

The vertex form of a parabola is
$\textcolor{w h i t e}{\text{XXXX}}$$m {\left(x - a\right)}^{2} + b$ with a vertex at $\left(a , b\right)$

Converting $y = {x}^{2} - 6 x + 10$ into vertex form:
$\textcolor{w h i t e}{\text{XXXX}}$Note $m = 1$ and we can continue with the rest of the conversion.
$\textcolor{w h i t e}{\text{XXXX}}$Complete the square
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$y = {x}^{2} - 6 x + 9 + 1$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{XXXX}}$$y = \left(x - 3\right) + 1$

and we can simply read off the vertex coordinates.