Question

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) = -16t2 + 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?

Answer 1

I graphed the equation and I got the maximum to be 0.5,36 and the two plots on the x axis is -1,0 and 2,0. Can someone help me try to figure out the domain?

Answer 2

@johnweldon1993 can you help me

Answer 3

So the maximum height occurs at x = 0.5

and the 2 places where the parabola passes through the x-axis are at -1 and 2

so



So as we can see 0.5 is directly in between the -1 and the 2

what does that mean?

well it means that if we travel 1.5 seconds from the start, we arrive at maximum height

\(\large -1 + 1.5 = 0.5\)

and if we travel another 1.5 seconds from there, we arrive back at the ground

\(\large 0.5 + 1.5 = 2\)

So the domain that would be used to go from the beginning to the middle would be

[-1 , 0.5) and the domain to go from the middle to the end would be (0.5 , 2]

Answer 4

Ok, I understand.. thank you :)