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A basketball is thrown upwards. The height f (t), in feet, of the basketball at time t, in seconds, is given by the following function:

f (t) = - 16t^2 + 16t + 32

Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?

A - 0.5 < t < 1

B - 0.5 < t < 2

C - 1 < t < 2

D - 1 < t < 1.5

The required domain is 0.5 < t < 2.

Step-by-step explanation:

Find the time of maximum height by converting to vertex form:

f (t) = - 16t^2 + 16t + 32

f (t) = - 16 (t^2 - t) + 32

= - 16 [ (t - 0.5) ^2 - 0.25) ] + 32

So the time at maximum height = 0.5 seconds.

To find the time t when it falls to the ground:

-16t^2 + 16t + 32 = 0

-16 (t^2 - t - 2) = 0

-16 (t - 2) (t + 1) = 0 giving t = 2, - 1 (we ignore the - 1).

t = 2 seconds.

Therefore the answer is 0.5 < t < 2.