Question

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 64t + 80 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

hold on

Answer 2

okay

Answer 3

f(x) = -16x^2 - 64x + 512

A)
f(x)
= -16(x^2 + 4x - 32)
= -16(x + 8)(x - 4)

x-intercepts are x=-8, x=4

B)
f(x)
= -16(x^2 + 4x + 4) + 64 + 256
= -16(x + 2)^2 + 320

The vertex is (-2,320)

C)
The axis of symmetry is x=-2

2)
9x^2 - 16x + 60 = 0

A)
b^2 - 4ac
= 16^2 - 4*9*60
= -1904

There is no solution

B)
4x^2 + 8x - 5 = 0
(2x + 5)(2x - 1) = 0
x = -5/2, x=1/2

I chose this method because it factored nicely.

C)
2x^2 -12x + 5 = 0
x = [12 ± √(12^2 - 4*2*5)]/(2*2)
= (12 ± √104)/4
= [12 ± √(4*26)]/4
= 3 ± √26/2
x = 0.4505 or x = 5.5495

Answer 4

there ya go

Answer 5

i got another question

Answer 6

ok

Answer 7

wait where did you get +512 from

Answer 8

ok i showed all my math

Answer 9

f(x) = -16x^2 - 64x + 512 you put this as the equation

Answer 10

yes i did

Answer 11

but its f(t) = -16t2 - 64t + 80

Answer 12

errrrr i tried

Answer 13

lol its okay