# How do you find the vertex and the intercepts for #f(x)=x^2-6x-6#?

##### 1 Answer

vertex:

y-intercept:

x-intercepts:

#### Explanation:

Given

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We can convert this into the general vertex form

by "completing the square" methodology:

which is the vertex form with vertex at

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The y-intercept (or equivalently the

is the value of

So the y (or

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The x-intercepts are the values of

So we want the values of

Since there is not obvious factoring of the left side,

we will use the quadratic formula to find the "roots" of this expression.

In this case

so we have

So the

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =