The equation is .

Let .

Therefore .

a. Determine whether the function has maximum or minimum value:

For  ,

Standard form equation .

Compare the above two equations, .

Because a is negative the graph opens down, so the function has a maximum value.

b. State the maximum or minimum value of the function:

The maximum value is y-coordinate of the vertex.

The x-coordinate of the vertex is  .

                              (Substitute )

                              (Product of two same signs is positive)

                                   (Multiply: )

                                     (Cancel common terms)

                (Original equation)

    (Substitute )

           (Evaluate powers: )

                   (Multiply: )

                                   (Add: )

The maximum value is 3.

c. State the domain and range of the function:

The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or .

a. a is negative the graph opens down, so the function has a maximum value.

b. The maximum value is 3.

c. The domain is all real numbers. The range is all real numbers less than or equal to the maximum value, or .