Question

I need help /.\
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?

0.5 < t < 1
0.5 < t < 2
1 < t < 2
1 < t < 1.5

Answer 1

I'm thinking 0.5 < t < 2

Answer 2

I'm just confused, fully with the entire thing. If you don't mind, could you help me with another question?

Answer 3

highest point should be the vertex and the rightest zero

x value of vertex = -b/2a given ax^2 + bx + c

so plug in and you will get your first point

Answer 4

the other point would be solve -16x^2 + 16x + 32 = 0
and take the positive answer, then you will get your other point

Answer 5

Ohhh okay.
I have one more question that I don't get, can you help me?

Answer 6

Yes I will help with what I can :)

Answer 7

Thank you ^.^
A punter kicks a football upward with an initial speed of 48 feet per second. After how many seconds does the ball hit the ground?

Use the formula h = rt − 16t2 where h represents height in feet and r represents the initial speed.

Answer 8

h = 0 when it hits the ground, therefore:
-16t^2 + 48t = 0

_________________________

Factor out -16t
-16t(t + 3) = 0
:
Two solutions
t = 0, when it begins it's upward journey
and
t = 3 sec, when it returns to earth

Answer 9

So the answer would end up being 3?

Answer 10

Yes :)

Answer 11

Okay, thank you so much! That last one was easier than I thought, I thought there were more steps cx

Answer 12

No problem :P