Question

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 384 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

well factor out -16 and you get

\[f(t) = -16(t^2 + 2t - 24)\]

now factor the quadratic

Answer 2

In part B it talks about f(x).... where does that come from... seeing the original equation is f(t)

Answer 3

Wait how did you get that for a?

Answer 4

well you need to factor the quadratic in the brackets for A

find the factors of -24 that add to 2... the larger factor is positive...

that should be relatively easy

Answer 5

How do I find the factor of -24?

Answer 6

start with what are the factors of 24...

Answer 7

What can be multiplied to get 24?

Answer 8

Hello, @campbell_st ?

Answer 9

thats correct... what pairs multiply to 24

or you can work on what pairs multiply ti -24 and have a difference of 2

e.g. 24 and -1 difference = 23 12 and -2 difference = 10

Answer 10

Ok, so those are the factors of 24.

Answer 11

they are some of the factors of -24... but not the ones you need... what other pairs multiply to -24...?

Answer 12

-4 * 6

Answer 13

OHHHH and that has 2 number difference

Answer 14

great so the factored form is

\[f(t) = -16(t + 6)(t - 4)\]

so what do they mean.... here is a simply sketch



the only intercept you need to consider is 4.... and you are talking time... and we can't go back in time so ignore -6 as an intercept...

so what do you think t = 4 represents...?