Question

The towers of a suspension bridge are 450 feet apart and 150 feet high from the roadway. Cables are at a height of 25 feet above the roadway, midway between the towers, but gradually get taller toward each end. Assume the x-axis is the roadway and the y-axis is the center of the bridge, write an equation for the parabola. What is the height of the cable at a point 50 feet from one of the towers? Round to the nearest whole number.

Answer 1

y = 1/405 x² + 25

101 feet

Explanation:

The vertex of the parabola is (0, 25).

The equation of the parabola is:

y − 25 = a (x − 0)²

y = ax² + 25

Two points on the parabola are (-225, 150) and (225, 150).

Plugging in one of those points:

150 = a (225)² + 25

125 = 50625 a

a = 1/405

The equation is therefore:

y = 1/405 x² + 25

50 feet from a tower is 175 feet from the center.

y = 1/405 (175)² + 25

y ≈ 101