A farmer has 90 feet of fencing with which to enclose two rectangular pens adjacent to a long existing wall, as shown below. He will use the wall for one side and the available fencing for the long side parallel to the wall and for the three fence portions perpendicular to the wall.

(a) If the sides perpendicular to the wall have length x feet, which of the following (A, B, C, or D) represents the area A of the whole enclosure (both pens combined)?

(no explanation required)

A. A(x) = -x2 - 45x
B. A(x) = -3x2 + 45x
C. A(x) = -3x2 + 90x
D. A(x) = 3x2 + 90x

The area function is a quadratic function and so its graph is a parabola.

(b) Does the parabola open up or down? __________

(c) Find the vertex of the quadratic function A(x).