Answer:
Maximum height reached is 256, units unspecified
Explanation:
there are two main ways this can be done:
Easy way: graph the function, and Identify the maximum or vertex. (3,256) thus the ball reaches the height of 256 units after 3 units of time.
real way: because sometimes graphing is not an option, the real way is to identify the maximum by taking the derivative.
step 1: find the function's derivative.
d'(t) = -32 t + 96 (power rules)
step two: set derivative equal to zero and solve
-32 t + 96 = 0
-32 t = -96
t = 3 (devide by -32)
thus, at t = 3, the original equation will be at its maximum.
original equation: h (t) = -16 t^2 + 96 t + 112
substitute 3 for t: h (3) = -16 (3)^2 + 96 (3) + 112
solve: h (3) = 256
thus, the maximum height the ball reaches is 256 units at 3 units of time.