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.

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

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

order of operations*

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

4^2=4(4)=16

16(4)^2=16(16)

ok i thought so

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

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

i don't have a calculator

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

don't you have a calculator on your computer?

yes but i don't like it

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

ohh right i forgot about the negative. thanks!!

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

how would i go about solving this one?

find the vertex of the parabola

...?

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

fmax i think

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

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

8

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

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

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

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

but 10/2 =5

so they both had the factor 16 in common

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

now complete the square inside that parenthesis

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

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