# How do you find the vertex of #y= (x-3)(x+3)#?

##### 2 Answers

Construct the vertex using part geometry and part algebra to find

#### Explanation:

This is a vertical parabola that cuts the

Since parabolas are symmetrical, its axis must be midway between these, namely the vertical line

The axis intersects the parabola at the vertex, so substitute

that is the point

graph{(x-3)(x+3) [-19.91, 20.09, -12.08, 7.92]}

Multiply out to find

giving

#### Explanation:

(use the difference of squares identity:

So

This takes minimum value when

When

So the vertex is at