Answer:
Given function:
f(t) = (-16t - 2)(t - 1)
Part 1
The zeros of the function are the values of t when f(t) = 0
⇒ f(t) = 0
⇒ (-16t - 2)(t - 1) = 0
⇒ (t - 1) = 0 ⇒ t = 1
⇒ (-16t - 2) = 0 ⇒ t = -2/16 = -1/8
Part 2
The zeroes tell us the time (in seconds) when the ball is at ground level (when its height is zero).
Since time is not negative, only one zero is meaningful: t = 1
Therefore, the total journey of the ball, from throwing it to it hitting the ground, is 1 second.
Part 3
The height the ball is thrown can be determined by inputting t = 0 into the function:
⇒ f(0) = (-16(0) - 2)(0 - 1)
⇒ f(0) = (0 - 2)(0 - 1)
⇒ f(0) = (-2)(-1)
⇒ f(0) = 2
Therefore, the height from which the beach ball is thrown is 2 ft.
