A parabolic arch sculpture is on top of a city bank. A model of the arch is y= -0.005x^2 + 0.5x were x and y are in feet.

Question

What is the distance from the highest point of the arch to the ground

What is the width of the bank.

Answer 1

h = -b/2a = -0.5/(2(-0.005)) = 50 ft

 

k = -0.005(2500) + 0.5(50) = 12.5 ft

 

The highest point is 12.5 ft plus the height of the bank to the ground, and since the vertex is midway between either end, the bank is 2(50) = 100 ft wide.