Question

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 128 shows the height f(t), in feet, of the sandbag after t seconds.
Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function. (4 points)

Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph? (4 points)

Part C: Use your answer in part B to determine the axis of symmetry for f(x)? (2 points)

Answer 1

yes def!

Answer 2

\[f(t)=-16t ^{2}-32t+128\]

Answer 3

I cant the policy says dont give direct answers without any working becuase thats cheating

Answer 4

\[-16(t ^{2}+2t-8)\]

Answer 5

\[-16(t +5)(t-3)\]

Answer 6

Yeah i get that part...

Answer 7

so f=0 when t=-5 or t=3, so the sandbags will land either "-5 seconds" later or 3 seconds later

Answer 8

obviously you want to throw out the negative answer

Answer 9

yeah the negative needs to go

Answer 10

I hate part B, becuase nobody complete square after they learn calculus, but I guess you can use calculus here

Answer 11

i never like these questions!

Answer 12

*cant

Answer 13

okay if you need to skip B we can go to C

Answer 14

I''ll just give you the answer by differentiating the function, you can complete the squares on your own and see if your answer matches mine

Answer 15

df/dt=-32t-32=0

Answer 16

so t=-1

Answer 17

and f=-16+32+128=144

Answer 18

so vertex is (-1,144)

Answer 19

and its clearly a max, since if the leading coeff is negative, the parabola opens downwards

Answer 20

just as a sanity check

Answer 21

d^2f/dt^2=-32,which is negative, and hence vertex is a maximum value

Answer 22

ok

Answer 23

symmetry is about t=-1

Answer 24

Yeah ik my mom just came in... its past my bedtime.. i gtg

Answer 25

Thank you! i gave you a fan + medal

Answer 26

Bye