Question

A basketball is thrown upwards. The height f(t), in feet, of the basketball at different times t, in seconds, is shown 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 highest height to the ground?

Answer 1

these are the choices:

0.5 ≤ x ≤ 1

0.5 ≤ x ≤ 2

1 ≤ x ≤ 2

1 ≤ x ≤ 1.5

Answer 2

@iambatman @sleepyhead314 @shamim @Loser66 @jim_thompson5910 someone please help!!!

Answer 3

highest point in this case should be the vertex and the rightest zero

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

Answer 4

plug in and that'll be the first point...

the other point would be solve -16x^2 + 16x + 32 = 0
and take the positive answer, that'll be your other point

Answer 5

okay one sec

Answer 6

okay the vertex is (0.5,36) ?

Answer 7

@sleepyhead314

Answer 8

um yeah, but you just need the x values to get domain

Answer 9

....oh

Answer 10

it's alright, you just did more work than you needed :P
no harm done
now solve -16x^2 + 16x + 32 = 0 and take the positive answer

Answer 11

how do i solve this? @sleepyhead314 what method do i use?

Answer 12

first factor out the greatest common factor (-16)
then factor... do you know how to do that? :3

Answer 13

i think so.. one moment (:

Answer 14

um i think i may ave used the wrong factoring method.. again.. i got
0=-16(t+0.5)+6

Answer 15

mmm that looks like vertex form :/
not quite
I'm trying to get at something like
(x+3)(x-2) = 0 -> x = -3, 2

Answer 16

Thanks! i definitely used vertex form, oops. so it is the second one right? (B)?

Answer 17

Correct! :)

Answer 18

Thank you so much!!! cx

Answer 19

I'm glad I could help ^_^

Answer 20

i have 2 more problems, think you could help me with them?

Answer 21

It's a bit past my bed time, but I can try :)