Question

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.

Answer 1

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

Answer 2

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

Answer 3

order of operations*

Answer 4

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

Answer 5

4^2=4(4)=16

Answer 6

16(4)^2=16(16)

Answer 7

ok i thought so

Answer 8

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

Answer 9

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

Answer 10

i don't have a calculator

Answer 11

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

Answer 12

don't you have a calculator on your computer?

Answer 13

yes but i don't like it

Answer 14

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

Answer 15

ohh right i forgot about the negative. thanks!!

Answer 16

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

Answer 17

how would i go about solving this one?

Answer 18

find the vertex of the parabola

Answer 19

...?

Answer 20

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

Answer 21

fmax i think

Answer 22

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

Answer 23

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

Answer 24

8

Answer 25

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

we need to factor out -16 out of first two terms

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

but 10/2 =5

Answer 30

so they both had the factor 16 in common

Answer 31

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

Answer 32

now complete the square inside that parenthesis

Answer 33

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