Question

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your rollercoaster I need help with this?

Answer 1

The factor theorem:
If \(a\) is a zero of \(f(x)\), then \((x-a)\) is one of its factors.

Answer 2

Maybe you should find out the factors of the polynomial function.

Answer 3

How do I turn these numbers into a polynomial function?

Answer 4

You multiply all its factors together, and expand.

Answer 5

so multiply 6 -2 and -7??

Answer 6

Nope, 6, -2 and -7 are not factors of f(x)

Answer 7

Please kindly read what I have written above

Answer 8

oh lol sorry! can you tell me how i find the factors?

Answer 9

The factor theorem:
If \(a\) is a zero of \(f(x)\), then \((x-a)\) is one of its factors.

Answer 10

For example, if 3 were one of its zeros, then (x-3) would be one of its factors.

Answer 11

I'm so confused lol I'm sorry

Answer 12

Can you just tell me what to do from the start and maybe I'll understand in the process

Answer 13

So you know that 6 is one of its zeros... what's its corresponding factor?

Answer 14

I just said that if 3 were one of its zeros, then (x-3) would be one of its factors

Answer 15

so it would be (x-6)?

Answer 16

Exactly

Answer 17

So what's the corresponding factors for -2 and -7?

Answer 18

x--2 and x--7?

Answer 19

which turn into positives right?

Answer 20

Yep, so you're getting it :)

Answer 21

so what do i do after i turn them into factors?>

Answer 22

What are the factors again?

Answer 23

thank you so much for helping right now lol i'm failing my math class right now and im in desperate need of help lol

Answer 24

(x-6) (x+3) (x+7)

Answer 25

One tiny typo out there, spot it :p

Answer 26

(x+2) lol sorry

Answer 27

Now expand it :)

Answer 28

what do you mean?

Answer 29

Expand (x-6)(x+2)(x+7)

Answer 30

how do i expand it

Answer 31

Well...

Answer 32

FOIL it?

Answer 33

do i multiply x by x?

Answer 34

Well... talking about expansion...

Answer 35

\[(x-6)(x+2)(x+7)\]\[=[x(x+2)-6(x+2)](x+7)\]\[=(x^2+2x-6x-12)(x+7)\]\[=(x^2-4x-12)(x+7)\]\[=x(x^2-4x-12)+7(x^2-4x-12)\]\[=x^3-4x^2-12x+7x^2-28x-84\]\[=x^3+3x^2-40x-84\]

Answer 36

Any step you don't understand?

Answer 37

I think that I get it

Answer 38

Glad to hear that

Answer 39

so is that all i do for this question?

Answer 40

Yep

Answer 41

thanks so much! do you think you can help me with the next question?

Answer 42

let me write all of this down first though so i know what i'm doing lol.

Answer 43

Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph

Answer 44

Where is the graph?

Answer 45

oh sorry hold on.

Answer 46

That ain't a graph?

Answer 47

that's whats with the assignment lol

Answer 48

then can you help[ with this one ts my last one? jSolve for the y–intercept for your function, f(x), and then construct a rough graph of your rollercoaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.

Answer 49

@kc_kennylau