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: )

                                 (Divide: )

               (Original equation)

   (Substitute )

           (Evaluate powers: )

                    (Multiply: )

                             (Add: )

The minimum value is .

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 .

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