The function models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff.
y=-16t^2 + 486
How long will it take for the stone to hit the ground?

Question

The function models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff.
y=-16t^2 + 486
How long will it take for the stone to hit the ground?

jdoe0001 · Answer

have you covered parabolas yet?

anonymous · Answer

Yes

jdoe0001 · Answer

well... notice on this one
the leading term is negative

meaning the parabola opens downward  |dw:1413328144162:dw|  so you're really asked what is "t" or the time, when the parabola touches the x-axis

or $\bf  y=-16t^2 + 486\implies 0=-16t^2 + 486\qquad \textit{what is }t?$

anonymous · Answer

ohhhh ok I get that part
I'm confused about what to do next @jdoe0001

anonymous · Answer

This quadratic equation is similar to a linear one except that now you will have to two values for t.

anonymous · Answer

ok

anonymous · Answer

BTW we are not here to provide you answers, we are here to help YOU get the answer, and clarify things.

anonymous · Answer

yes i know.
i got an answer, but it is not even close to any of the four answer choices provided

anonymous · Answer

can you tell us what you did, so we can find the mistake and correct you.

anonymous · Answer

I used -16t^2 + 486 = 0
then factored that to: -2(8t^2 - 243) = 0

anonymous · Answer

okay dont factor out 2. just move the 486 to the other side, and treat it like a linear equation. except that you will have a negative and positive answer, since you are going to be square rooting it.

anonymous · Answer

so just -16t^2 = -486

anonymous · Answer

yup, isolate for t^2 now. and then square root the both side to get just t=the answer.

anonymous · Answer

so id divide by -16 on both sides?

anonymous · Answer

yup

jdoe0001 · Answer

$\bf 0=-16t^2+486\implies -486=-16t^2\implies \cfrac{\cancel{ -486 }}{\cancel{ -16 }}=t^2
\ \quad \
\sqrt{\cfrac{\square }{\square }}=t$

jdoe0001 · Answer

well..   $\bf 0=-16t^2+486\implies -486=-16t^2\implies \cfrac{\cancel{ -486 }}{\cancel{ -16 }}=t^2
\ \quad \
\pm \sqrt{\cfrac{\square }{\square }}=t$

anonymous · Answer

so t^2 = 30.375

anonymous · Answer

t=5.51
got it

jdoe0001 · Answer

what answer choices did you get?

anonymous · Answer

Oh and never choose the negative answer for time, since you cannot have a negative time.

anonymous · Answer

5.51 was one of them

anonymous · Answer

yes

jdoe0001 · Answer

k