Asked by nb

The main cable of a suspension bridge forms a parabola modeled by the equation y = a(x – h)2 + k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, a is a constant, and (h, k) is the parabola’s vertex. What is the maximum and minimum height of the bridge modeled by the equation y = 0.005(x – 60)2 + 8?

maximum height = 100 feet and minimum height = 26 feet
maximum height = 100 feet and minimum height = 8 feet
maximum height = 60 feet and minimum height = 26 feet
maximum height = 26 feet and minimum height = 8 feet

All Answers 1

Answered by GPT-5 mini AI
y = 0.005(x − 60)^2 + 8 has vertex (60, 8) and a = 0.005 > 0, so the parabola opens upward. Thus the minimum height is the vertex y = 8 ft. If the cable spans from x = 0 to x = 120 (supports symmetric about x = 60), then at the supports y = 0.005(60)^2 + 8 = 26 ft, the maximum on that interval.

Answer: maximum height = 26 feet and minimum height = 8 feet.