The quadratic function is .

For this function a = 3 , so the graph opens up and the function has a minimum value. \ \

The minimum value of the function is the y-coordinate of the vertex.

The - coordinate of the vertex is .

               (Substitute the values a = 3 and b = 8)

       (Simplify) \ \ The y-coordinate of the vertex by evaluating the function for = . \ \

                   (Original function)

    ( =   )

           (Simplify)

or

The minimum value of the function is .

\ \

The domain is all real numbers.

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

\ \

The function has minimum value.

The minimum value of the function is . \ \

The domain is all real numbers.

The range is . \ \