l +2w = 500
a = lw
a) l = 500 -2w
.. a = (500 -2w)*w
b) The zeros of the above equation are w=0, w=250. The vertex of this quadratic is on the line of symmetry, halftway between the zeros, at w=125 ft.
c) a = (500 -2*125)*125 = 31,250 . . . . square feet