Ihave another : /

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.

(-1,-0.5)

step-by-step explanation:

step-by-step explanation: