Question

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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

Answer 1

The required domain is 0.5 < t < 2

Explanation:

The required domain is 0.5 < t < 2

got it right 5/22

Answer 2

The required domain is 0.5 < t < 2.

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.