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) = -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

@math&ing001

Answer 2

Same, you find the vertex

Answer 3

the vertex is 1/2 but I dont see that as an option

Answer 4

Then you find the time when the basketball hits the groung (aka solve f(t)=0)

Answer 5

1/2 = 0.5

Answer 6

Oh ok let me try that

Answer 7

sorry I did't see the 0.5

Answer 8

f(0) = -16(0)^2 + 16(0) + 32
f(0) = 32

Answer 9

no f(t)=0 and you solve for t

Answer 10

what do you mean. Can you explain that please?

Answer 11

f(t)=0 ie -16t^2 + 16t + 32 = 0
We solve the quadratic equation

Answer 12

oh ok I learned this in my class but it was kid of confusing so can you explain how I am supposed to solve this?

Answer 13

Im sorry im really not that great at math

Answer 14

You might wanna check this http://www.purplemath.com/modules/quadform.htm

Answer 15

so would I substitute the numbers into the quadratic formula?

Answer 16

Yep !

Answer 17

ok let me try:
x = -16 ± √16^2 - 4(-16)(32) / 2(-16)
x = -16 ± √256 - (-2048) / -32
x = -16 ± √2304 / -32
x = -16 ± 48 / -32
x = -16 + 48 / -32 And -16 - 48 / -32
x = -1 AND x = 2

Answer 18

Correct but time can't be negative so x=2

Answer 19

ok so the answer would be option 2?

Answer 20

Correct

Answer 21

Thank You so much!!!

Answer 22

Welcome !!