Question

Can someone help I will give medal I don't not understand how to do this
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

Part A
start here

\(\large f(t) = -16t^2 - 32t + 384 = -16(t^2 +2t - 24) \)

now make it \(\large f(t) = -16(t-a)(t-b) \)

ie factor it. x = a and x = b are where f(t) = 0.

Answer 2

Do I factor -16 with (t-a)(t-b)?

Answer 3

a made up example:
\(\large f(t) = - 15 (t^2 + t - 6) = -15(t-2)(t+3)\)

so, in our example, we know that f(t) = 0 at t = 2 and t = -3 [ or f(2) = f(-3) = 0 ]

it will hit the ground at t = 2.

t = -3 is something that existed before it was dropped and we can guess that it would have taken 3 second to have risen to its drop height at t = 0. if that makes sense :p

Answer 4

Yes that makes sense

Answer 5

so you have to do that for the actual question above

pattern match with the example if need be

Answer 6

Okay. Thank you so much!! :-)

Answer 7

mp