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H ( t ) = − 16 t 2 + 96 t + 112

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5 votes

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.

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