Question

A sandbag was thrown downward from a building . The function f(t)=-16t^2-32+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.
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?
Part C: Use your answer in part B to determine the axis of symmetry for f(x).

Answer 1

@welshfella do you think you could help?

Answer 2

@Hero @mathstudent55 @iGreen

Answer 3

I think I have some of Part A but I'm not sure if I'm right

Answer 4

i think the function should be

-16t^2 -32t + 384

Answer 5

Oops yeah
I did this for part A:

Answer 6

this factors to

-16(t^2 +2t - 24)

Answer 7

yes you are right

Answer 8

What does it mean to use the factors to interpret the meaning of the x-intercept?

Answer 9

the x -intercepts on the graph of this function represent the time when f(t) = 0
- that is when the sandbag reaches the ground

Answer 10

Now Part B?

Answer 11

so thats is when t = 4 or t = -6 (we can ignore the -6)

Answer 12

Wait, what do I write for B?

Answer 13

as the coefficient of x is negative the graph is a parabola which opens downwards and it will have a maximum value.

Answer 14

you can complete the square by first halving the coefficient of x and proceed as follows
-16(t^2 +2t - 24)

= -16 [(t + 1)^2 - 1 - 24] ( half of the 2 in 2t)
= -16 [(t + 1)^2 - 25]

Answer 15

You lost me there now ._.

Answer 16

you ok about -16(t^2 + 2t - 24) ?

Answer 17

Yeah, I know how to get that, but everything else got wayyy too complicated

Answer 18

do you think you could write it out step by step?

Answer 19

yes ok

the vertex form of a trinomial function is

(x - a)^2 + b

where a is the x coordinate of the axis of symmetry and b is the vertex