I'm a bit confused ;~;

Question

party_girl · Answer

About what?

camerondoherty · Answer

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?

camerondoherty · Answer

It's k c:

anonymous · Answer

no it is not  all real numbers

camerondoherty · Answer

It isn't?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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 
$$-16t^2+94t+12=0$$

camerondoherty · Answer

Ok, gimme a sec

camerondoherty · Answer

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

anonymous · Answer

something like that

camerondoherty · Answer

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

camerondoherty · Answer

Then plug that solution into the original equation?

anonymous · Answer

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

anonymous · Answer

denominator should have been 32 but yeah you are right

camerondoherty · Answer

So:
$$f(t)=−16(2.9375)^2+94(2.9375)+12$$

anonymous · Answer

yeah but you don't need that number

anonymous · Answer

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

anonymous · Answer

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

camerondoherty · Answer

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

anonymous · Answer

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

camerondoherty · Answer

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

camerondoherty · Answer

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?

anonymous · Answer

i would go with $3<t<6$

anonymous · Answer

time it is highest to time it hits the ground

camerondoherty · Answer

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

camerondoherty · Answer

And it hits the ground at 0?

anonymous · Answer

greater than 3 and less than 6

camerondoherty · Answer

Thats what I meant, sorry, typo, lol

anonymous · Answer

it  hits the ground if the height is zero
 $h=0$ when $t=6$

camerondoherty · Answer

Oh I see!
Thank You! c:

anonymous · Answer

yw