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:

Answer 1

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 2

Do you know how to factor?

Answer 3

a little bit

Answer 4

@ganeshie8
@tHe_FiZiCx99
@jim_thompson5910
@bahrom7893
@iambatman
@Ashleyisakitty

Answer 5

-16t^2 - 32t + 128
Factor out -16 first. What do you get?

Answer 6

I don't know

Answer 7

Take -16 out and divide each coefficient by -16

Answer 8

2?

Answer 9

There are 3 coefficients: -16, -32, +128
When you factor out -16 you have to divide each coefficient by -16.

Answer 10

oooohh okay

Answer 11

@ranga now what do I do?

Answer 12

Factor out -16 from -16t^2 - 32t + 128 by dividing each coefficient by -16:
-16t^2 - 32t + 128 = -16( ? t^2 + ? t + ?)
fill in the 3 question marks by dividing the corresponding coefficient by -16

Answer 13

what do I do now?*

Answer 14

You should know how to factor out a constant by now. You may want to brush up because you are likely to come across factoring again and again.

Answer 15

−16(t+4)(t−2)

Answer 16

Yes.

Answer 17

x-intercept is when f(t) = 0
-16(t+4)(t-2) = 0
t = ?

Answer 18

idk :/

Answer 19

If (x+a)(x+b) = 0 it implies
x + a = 0 or x + b = 0
x = -a or x = -b

Answer 20

ok..

Answer 21

-16(t+4)(t-2) = 0 when t = ?

Answer 22

-4?

Answer 23

-6?

Answer 24

-16(t+4)(t-2) = 0 implies
t + 4 = 0 OR t - 2 = 0
t = -4 OR t = 2
Here t is a measure of time in seconds. So negative time does not make sense and can be ignored. t = 2 seconds is the solution.
"interpret the meaning of the x-intercept of the function"
x-intercept is when y or f(t) is zero. Therefore, when t = 2, f(t) = 0.
f(t) is the height of the sandbag at time t.
f(t) = 0 implies the height is zero or the sandbag hits the ground.
So at t = 2 seconds, the sandbag reaches the ground.

Answer 25

ok

Answer 26

f(t) = -16t^2 - 32t + 128 = −16(t+4)(t−2) = -16( t^2 + 2t - 8)
complete the square of ( t^2 + 2t - 8)

Answer 27

wait what????

Answer 28

In part A I ask you to factor -16 out of -16t^2 - 32t + 128.
-16t^2 - 32t + 128 = -16(t^2 + 2t - 8)
In part B they are asking you to complete the square.
So complete the square of ( t^2 + 2t - 8)

Answer 29

i don't remember the complete the square method

Answer 30

take the coefficient of the middle term and divide by 2
t^2 + 2t - 8. Coefficient of middle term is +2. Divide by 2 to get 1.
This 1 will go inside the parenthesis to be squared and outside you have to subtract 1^2
t^2 + 2t - 8 = (t + 1)^2 - 1^2 - 8 = (t + 1)^2 - 9
f(t) = -16t^2 - 32t + 128 = -16(t^2 + 2t - 8) = -16{ (t + 1)^2 - 9 } =
f(t) = -16(t+1)^2 + 144
compare this to the vertex for of a parabola y = a(x-h)^2 + k where (h,k) is the vertex and you get h = -1 and k = 144.
So the vertex is at (-1, 144).

The vertex will be a maximum because the leading coefficient of the parabola is -16 which is negative and therefore the parabola open downward which means the vertex is a maximum

Answer 31

Part C) This is a vertical parabola which means the axis of symmetry will be a VERTICAL line passing through the vertex. The equation of a vertical line passing through (-1, 144) is x = -1.

Answer 32

thanks i appreciate the help