Chapter 4.1, Problem 74E

Highway Design la order to build a highway, it is necessary to fill a section of a v alley 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 arc that is tangent to the two slopes at the points A and B. The horizontal distances from A to the y axis and from R to the y axis are both 500 feet.

(a) Find the coordinates of A and A

(b) Hind a quadratic function $y=a{x}^{2}bx+c$ for $-500\le x\le 500$ that describes the top of the filled

region.

(c) Construct a table giving the depths d of the fill for

$x=-500,-400,-300,200,-100,0,200,300,400,\text{and}500$

(d) What will be the lowest point on the completed highway? Will it be directly over the point where the two hillsides come together'.'