# What is the the vertex of #y = (x -3)^2-9x+5 #?

##### 1 Answer

Vertex at :

#### Explanation:

Given

Expanding:

We can proceed from here in 2 ways:

- by converting this into
*vertex form*through "completing the square" method - using the axis of symmetry (below)

**Using the axis of symmetry**

Factoring we have

which implies

The axis of symmetry passes through the midpoint between the zeros

i.e. the axis of symmetry is

Note that the axis of symmetry also passes through the vertex;

so we can solve the original equation (or more easily our factored version) for the value of

So the vertex is at

We can verify this result with a graph of the original equation:

graph{(x-3)^2-9x+5 [-0.016, 14.034, -45.34, -38.32]}