Answer:
f(x) = x^2/500 + 5
f(100) = 100^2/500+5 = 25
Cable is 25 feet above road 100 feet from center of bridge.
Step-by-step explanation:
Assume towers are 50 feet above the road and the road is flat and level.
Tower bases are (-150,0) and (150,0).
Tower tops are (-150,50) and (150,50).
Center of bridge at roadway is (0,0).
Minimum height of parabola is (0,5).
f(x) = ax^2 + bx + c
The parabola is symmetrical about the y axis so b = 0
Constant term c = 5.
f(0)=5
f(150)=f(-150)=50.
a × 150^2 + 5 = 50
a = 45/(150^2) = 5/(50^2) = 1/500
f(x) = x^2/500 + 5
f(150) = 150^2/500+5 = 50✔
f(100) = 100^2/500+5 = 25
