Question

Algebra Factoring question Will Give Fan and Medal!

Answer 1

A sandbag was thrown downward from a building. The function f(t) = -16t^2 - 32t + 384 shows the height f(t), in feet, of the sandbag after t seconds:

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

@ganeshie8 @iambatman

Answer 3

@bohotness can you help?

Answer 4

go to brain fuse tulsa library look on google idk the answer their help you :)

Answer 5

Okay, Thank you tho @bohotness

Answer 6

@jim_thompson5910 do you think you can help?

Answer 7

yw

Answer 8

-16t^2 - 32t + 384 or -16x^2 - 32x + 384

is in the form ax^2 + bx + c

what are the values of 'a', 'b', 'c' ?

Answer 9

a=-16
b=-32
c=384

Answer 10

plug a = -16 and b = -32 into the formula x = -b/(2a) and tell me what you get

Answer 11

okay

Answer 12

I got 1 as my answer

Answer 13

close but no

Answer 14

did I get the sign wrong?

Answer 15

yeah you lost a sign somewhere

Answer 16

oh okay then it would come out as -1

Answer 17

sorry about that

Answer 18

the x coordinate of the vertex is -1

Answer 19

plug x = -1 into y = -16x^2 - 32x + 384 to get the y coordinate of the vertex

Answer 20

okay, But what does it mean in the question with complete the square?

Answer 21

what do you get for y?

Answer 22

336

Answer 23

incorrect

Answer 24

oh wait sorry

Answer 25

would it be 400?

Answer 26

yes so the vertex is (-1,400)

Answer 27

in general, the vertex is (h,k)

so h = -1 and k = 400

Answer 28

vertex form is y = a(x-h)^2 + k

Answer 29

the value of 'a' is already given (a = -16)

Answer 30

so now plug in the values into the equation?

Answer 31

yes

Answer 32

okay so it would be y=-16(x-(-1)0^2+400
What would be x? or is it not given?

Answer 33

x is a variable and it is unknown (and can change)

Answer 34

so the equation is either y = -16(x - (-1))^2 + 400 or y = -16(x +1)^2 + 400

the simplified version is always best

Answer 35

you could optionally change x to t and change y to f(t)

but that's a trivial step really

Answer 36

So the answer to part B would be y = -16(x +1)^2 + 400

Answer 37

well they say to complete the square. That gives you y = -16(x +1)^2 + 400 or f(t) = -16(t +1)^2 + 400

Answer 38

you then use this to determine the vertex which is (-1,400)

Answer 39

but you found the vertex first to get the vertex form

Answer 40

they ultimately want the vertex and want to know if it is a min or max

Answer 41

it would be maximum since y is positive. But the question says something about comlpeting the square.. How would I do that? Or have we already done it?

Answer 42

when you go from -16x^2 - 32x + 384 to y = -16(x +1)^2 + 400

you have completed the square

Answer 43

there is another method, but I don't like that method because it's a lot uglier in general

Answer 44

so when you go from standard form y = ax^2 + bx + c to vertex form y = a(x-h)^2 + k, you have completed the square

Answer 45

btw, it's not a max because y is positive

it is a max because 'a' is negative.

a = -16
a < 0
'a' is negative which means the vertex is a maximum point

Answer 46

the negative 'a' value graphs an upside down parabola with the max point at the very top