parabolic arches

Question

The height y of a parabolic arch is given by y= - 1/16 t² + 40, where x is the horizontal distance from the center of the base of the arch. All distances are in feet. What is the highest point on the arch? How wide is the arch at the base to the nearest tenth of a foot?

Answer 1

Since there is no middle term, one can determine the highest point of the arch occurs when x=0. Hence, the highest point of the arch is y=-1/16 *0^2+40=40 ft.

 

To determine how wide is the arch is to find what value of x is when y equals zero: Hence,

 

0=-1/16 x² + 40

40=1/16 x² Multiply both sides by 16

 

x²=640 Take the square root of both sides.

x=25.3 ft. Hence, the arch is about 25.3 feet wide.