# How do you find the vertex of  y = x^2 – 6x + 5 ?

Apr 2, 2016

Complete the square

#### Explanation:

After completing the square,

$y = {x}^{2} - 6 x + 5$

$= {\left(x - 3\right)}^{2} - 4$

Here is a graph of $y = {x}^{2} - 6 x + 5$.
graph{x^2 - 6x + 5 [-2, 8, -5, 5]}
We can see (either graphically or algebraically) that the lowest point, or minimum, occurs when $x = 3$ and $y = - 4$. That is the location of the vertex.

The coordinate of the vertex is $\left(3 , - 4\right)$.