# How do you find the axis of symmetry, and the maximum or minimum value of the function # f(x)=-x^2+6x+6#?

##### 2 Answers

Complete the square

The line

The maximum is

#### Explanation:

Completing the square gives

#f(x) = -(x-3)^2 + 15# .

Notice that

#f(3+a) = f(3-a)#

for any

Therefore, the line

The maximum is

This is because

#f(3)=15>=15-(x-3)^2=f(x)#

Axis of symmetry is

The maximum

#### Explanation:

As the coefficient for

Finding axis of symmetry: Let us look at the part of the equation that is

Compere to the standard form

Write standard form as:

From this

So in your case, as

But

Now it is just a matter of substituting