62. Highway Design In order to build a highway, it is necessary to fill a section of a valley where the grades (slopes) of the sides are 9% and 6% (see figure). The top of the filled region will have the shape of a parabolic are that is tangent to the two slopes at the points A and B. The horizontal distances from A to the y-axis and from B to the y-axis are both 500 feet. 500 ft 500 ft Highway 9% grade Not drawn to scale (a) Find the coordinates of A and B. 6% grade (b) Find a quadratic function y = ax2 + bx + c for -500 x 500 that describes the top of the filled region. (c) Construct a table giving the depths d of the fill for x = -500, -400,- 300,- 200,-100, 0, 100, 200, 300, 400, and 500. (d) What will be the lowest point on the completed highway? Will it be directly over the point where the two hillsides come together?