A parabolic arch spans a stream 220 feet wide. How high above the stream must the arch be to give a minimum clearance of 20 feet over a channel in the center that is 180 feet wide?
A) 20 feet
B) 31.325 feet
C) 60.5 feet
D) 80.5 feet
E) 34.725 feet

Question

Quizplus · Accepted Answer

The arch must be high enough so that the lowest point of the arch over the 180-foot wide channel is at least 20 feet. The parabola's vertex is at the center of the 220-foot span, so the equation is y = a(x - 110)^2 + h. The channel extends 90 feet on either side of the center, so at x = 20 and x = 200, y must be 20 feet. Solving for h gives h = 60.5 feet.

A Parabolic Arch Spans a Stream 220 Feet Wide