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

##### 1 Answer

Vertex at the point

#### Explanation:

**Let's first have a look at the #x# intercepts of the function:**

**Recall that the difference between two squares can be expressed as: #n^2-m^2=(n-m)(n+m)#**

If we consider 6 as:

We can now convert the function to a *difference of squares:*

* Using the Null Factor Law* we can now solve for

Therefore

**Let's now have a look at the #y# intercept of the function:**

Consider that for any function,

Therefore, the

**Finally, let's have a look at the vertex of the function:**

Consider the general form of a parabolic function:

If we compare the equation that you have presented:

We can determine that:

The

The

The constant term is

Therefore, we can use the formula:

to determine the

Substituting the appropriate values into the formula we get:

Substituting this value into the given function, we get:

Therefore, the vertex of the function is present at the point