Question

) The main cables of a suspension bridge are 20 meters above the road at the towers and 4 meters above the road at the center. The road is 80 meters long. Vertical cables are spaced every 10 meters. The main cables hang in the shape of a parabola. Find the equation of the parabola. Then, determine how high the main cable is 20 meters from the center

Answer 1

origin at center of roadway, 40 meters from each end. and at height of road

points
(-40,20), (0,4)which is vertex, (40,20)

(y -4) = k x^2
16 = k (40)^2
k = 16/1600 = .01
so
y = .01 x^2 + 4
==============================
at x = 20
y = .01(400) + 4 = 8