# How do you find the vertex of #g(x) = x^2 - 9x + 2#?

##### 1 Answer

Often the easiest way to find the vertex for a given parabolic equation is to convert it into vertex form.

#### Explanation:

The vertex form of a parabolic equation is

which has its vertex at

The following process is commonly called **completing the square**

Given

we can assume

To get the

we need to re-write the expression so it contains a squared binomial).

For the given expression the first two terms:

which implies

and the third term of the expanded binomial must be:

We want:

but instead of the

The solution?

Add in the

which can then be written as

Comparing this to the general vertex form,

we see the vertex is at

We can compare this result with the graph of the given function to see that our result is reasonable

graph{x^2-9x+2 [-3.82, 10.23, -20.15, -13.127]}