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Mathematics
OpenStudy (anonymous):

A toy rocket is launched off a 96-foot tall building. The rocket's height in feet h(t) is h(t) = -16t^2 + 80t + 96. Evaluate h(4). Explain what the answer means in terms of the toy rocket.

myininaya (myininaya):

h(4)=-16(4)^2+80(4)+96 simplify that by using order or operations

myininaya (myininaya):

at t=4, the height of the rocket is h(4) feet

myininaya (myininaya):

order of operations*

OpenStudy (anonymous):

does 16(4)^2 = 16 times 8 or 64^2?

myininaya (myininaya):

4^2=4(4)=16

myininaya (myininaya):

16(4)^2=16(16)

OpenStudy (anonymous):

ok i thought so

myininaya (myininaya):

-16(4)^2=-16(16)

OpenStudy (anonymous):

wait... when i solved it i got h(4) =652. is that correct?

myininaya (myininaya):

i don't have a calculator

myininaya (myininaya):

and i don't feel like doing the arithmetic by hand

OpenStudy (anonymous):

don't you have a calculator on your computer?

myininaya (myininaya):

yes but i don't like it

OpenStudy (dumbcow):

no, h(4) = 416-256 = 160

OpenStudy (anonymous):

ohh right i forgot about the negative. thanks!!

OpenStudy (anonymous):

now, they're asking me.... what is the toy rocket's maximum height? at what time does this occur?

OpenStudy (anonymous):

how would i go about solving this one?

myininaya (myininaya):

find the vertex of the parabola

OpenStudy (anonymous):

...?

myininaya (myininaya):

write in h(x)=a(x-h)^2+k form the vertex is (h,k) the height is k

OpenStudy (anonymous):

fmax i think

OpenStudy (anonymous):

so could someone show me how to plug it into this formula? i'm lost :'/

myininaya (myininaya):

you have to put in that form not plug it into that form

OpenStudy (anonymous):

8

myininaya (myininaya):

\[h(x)=(-16t^2+80t)+96 \] we need to factor out -16 out of first two terms

myininaya (myininaya):

\[h(x)=-16(t^2-\frac{80}{16}t)+96\]

myininaya (myininaya):

so divide both 80 and 16 by 8 to reduce the fraction 80/16

myininaya (myininaya):

\[h(t)=-16(t^2-\frac{10}{2}t)+96\]

myininaya (myininaya):

but 10/2 =5

myininaya (myininaya):

so they both had the factor 16 in common

myininaya (myininaya):

\[h(t)=-16(t^2-5t)+96\]

myininaya (myininaya):

now complete the square inside that parenthesis

myininaya (myininaya):

so what do we need to put in this blank to complete the square: \[t^2-5t+__\]

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