Answer Happy

11. [-/1 Points] DETAILS LARCALCET7 4.1.074. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER In order to build a highway, it is necessary to fill a section of a valley where the grades (slopes) of the sides are p% and q%, where p = 6 and q= 4 (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 B to the y-axis are both 500 feet, (a) Find the coordinates of A. (x, y) = 500 500 f Highway Find the coordinates of B. (x, y) = ( (b) Find a quadratic function yax2 + bx+c for-500 ≤ x ≤ 500 that describes the top of the filled region. y= (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. (Round your answers to two decimal places.) x-500 -400 -300 d x 100 d 200 300 -200 400 (d) What will be the lowest point on the completed highway? (x, y) = Will it be directly over the point where the two hillsides come together? Yes No -100 500 0