Problems Involving Conic Sections PARABOLA

Question

1. A gateway is a parabolic shape whose vertex is 20 𝑓𝑡. from the ground, (0,20), and the width on the ground is 25 𝑓𝑡. What is the maximum height of a vehicle to cross the gateway if it is 7 𝑓𝑡 wide? Find the standard equation the models the gateway
2. The cables of the suspension bridge are in the shape of parabola. The towers supporting the cable are 100 ft. apart and 100 ft. long. If the cables are at height of 10 ft. midway between the towers, what is the height of the cable at a point 50 ft. from the center of the bridge? What is the standard equation of the parabola that models a cable?

Please help! I'll really appreciate it.

Answer 1

f(x) = ax² + 20

0 = a(12.5)² + 20

-20 / (12.5)² = a

(Use same process for bridge problem)

Substitute value of a into

f(3.5) = a(3.5)² + 20