Question

The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 80 feet per second is f (t) = -16t2 + 80t + 6. (a) Verify that f(2) = f(3).

Answer 1

f(2) = f(3) = 102 ft

Explanation:

The height f at t = 2 seconds is given by:

`f(t) = -16t^2 + 80t + 6\\f(2) = -16*2^2 + 80*2 + 6\\f(2)=-64+160+6\\f(2)=102\ ft`

The height f at t = 3 seconds is given by:

`f(t) = -16t^2 + 80t + 6\\f(3) = -16*3^2 + 80*3 + 6\\f(3)=-144+240+6\\f(3)=102\ ft`

For both t =2 and t =3, the expression results in a height of 102 ft, therefore f(2) = f(3) = 102 ft.