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 positive the graph opens up, so the function has a minimum value.

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

The minimum value is y-coordinate of the vertex.

The x-coordinate of the vertex is  .

                          (Substitute )

                               (Multiply: )

                                  (Cancel common terms)

              (Original equation)

(Substitute )

     (Evaluate powers: )

           (Apply multiplicative identity property: )

                   (Multiply: )

                     (Subtract: )

                               (Add: )

The minimum value is 4.

c. State the domain and range of the function:

The domain is all real numbers. The range is all real numbers greater than or equal to the minimum value, or .

a. a is positive the graph opens up, so the function has a minimum value.

b. The minimum value is 4.

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