The equation h = -16t 2+ 53x + 8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked. What is the maximum height the football reaches?

The maximum height the football reaches = 51.89 feet.

Step-by-step explanation:

Given: The equation gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.

Differentiate the given equation, we get

  (i)

Put

Differentiate (i) w.r.t. t, we get

< 0  i.e. h is maximum at t= 1.65625

The value of h at t= 1.65625 will be

Hence, the maximum height the football reaches = 51.89 feet.

the final function for the graph becomes x-2=-1. before graphing you solve the equation, where x=1. then graph accordingly.   ( on the x-axis, 1 on the line will possess a vertical line.)