Solve.
-A cross-section of an irrigation canal is a parabola. If the surface of the water is 45 ft wide and the canal is 37 ft deep at the center, how deep is it 4 ft from the edge?
A) 12 ft
B) 30.7 ft
C) 6.3 ft
D) 25 ft

Question

Quizplus · Accepted Answer

The correct answer is A.The equation of the parabola is y = ax^2 + bx + c. Since the vertex is at (0, 0), we have c = 0. Since the width is 45 ft, we have 22.5 = a(22.5)^2 + b(22.5) + 0. Solving for a, we get a = -1/225. Since the depth at the center is 37 ft, we have 37 = a(0)^2 + b(0) + 0. Solving for b, we get b = 37. Therefore, the equation of the parabola is y = -x^2/225 + 37. When x = 4, we have y = -4^2/225 + 37 = 12.

Solve. -A Cross-Section of an Irrigation Canal Is a Parabola. If