Question

I'm a bit confused ;~;

Answer 1

About what?

Answer 2

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:
\[f(t) = -16t^2 + 94t + 12\]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?

3 < t < 6
2 < t < 5
1 < t < 4
0 < t < 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~
But wouldn't it be all real numbers?

Answer 3

It's k c:

Answer 4

no it is not all real numbers

Answer 5

It isn't?

Answer 6

domain of the graph of the function when the basketball falls from its maximum height to the ground?

Answer 7

first off \(t\) is time so even without that stipulation it would only be from 0 to when it hit the ground

Answer 8

you need two numbers
the first coordinate of the vertex when the height is the maximum, and also the time when it hits the ground, i.e the value of \(t\) for which
\[-16t^2+94t+12=0\]

Answer 9

Ok, gimme a sec

Answer 10

Sorry, I'm a bit slow at calculating cx
So would the vertex be (2.9, 150.06)?

Answer 11

something like that

Answer 12

So don't you plug that into the equation -b/2a?

Answer 13

Then plug that solution into the original equation?

Answer 14

\(-\frac{b}{2a}=\frac{94}{35}=2.9375\)

Answer 15

denominator should have been 32 but yeah you are right

Answer 16

So:
\[f(t)=−16(2.9375)^2+94(2.9375)+12\]

Answer 17

yeah but you don't need that number

Answer 18

you are only asked for the "domain" from the max height to when it its the ground

Answer 19

that number is the left hand endpoint, which from your answer choices looks like they want rounded to \(3\)

Answer 20

I put it into desmos, if that helps in any way:
http://prntscr.com/5u0e5i

Answer 21

no doesn't help much
here is a nice picture
http://www.wolframalpha.com/input/?i=-16x^2%2B94x%2B12

Answer 22

That other point is (6,0) but it was overlapping the other values
And ok cx

Answer 23

So, since the time would start at 0, and since when you plug the values into the equation: -b/2a it came out to 2.9, which was rounded to 3, would it be D?

Answer 24

i would go with \(3<t<6\)

Answer 25

time it is highest to time it hits the ground

Answer 26

Oh because the time would be less than three and less than 6

Answer 27

And it hits the ground at 0?

Answer 28

greater than 3 and less than 6

Answer 29

Thats what I meant, sorry, typo, lol

Answer 30

it hits the ground if the height is zero
\(h=0\) when \(t=6\)

Answer 31

Oh I see!
Thank You! c:

Answer 32

yw