The height y of a parabolic arch is given by y = -1/16 x2 + 40 a. What is the highest point on the arch? b. How wide is the arch at the base to the nearest tenth of a foot?

Answer 1

y = -x^2/16 + 40

To find the highest point, take the first derivative and set = 0

y' = -2x/16 = -x/8 = 0, then x=0

or this is an upside down parabola and is symmetric around the y axis.

Setting x=0 yields the highest point.

So the highest point is when x = zero, so y(0) = 0 + 40 = 40 ft high

The widest point is on the x axis or y = 0,

0 = -x^2/16 + 40

x^2 = 40(16) = 640

x = 25.3 ft wide