Question

I've been trying this one for hours ;-; can someone please help me I will medal and fan!
The shape of a roller coaster is modeled by a polynomial function, R(x). Describe how to find the x-intercepts of R(x) and how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster. You may create a sample polynomial to be used in your explanations.

Answer 1

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Answer 2

Let me explain with this fourth degree of the polynomial.
Let's take R(x) = 2x^4 + 3x^3 -11x^2 -9x +15
Now let's find the roots of R(x).
By default, let's check with x =1 or x = -1
Let x= 1
R(X) = 2(1)^4 + 3(1)^3 -11(1)^2 - 9(1) + 15
= 2+3-11-9 + 15
= 20 -20
= 0
So R(x) = 0 when x = 1
So x = 1 is one of the root.
So (x -1) is a factor.
Therefore R(x) = (x -1)(2x^3 + 5x^2 - 6x - 15)
To find the other roots, let's use RATIONAL ROOTS test.
Let me define the rational root test.
The roots will be fractions of the form= ± (factor of the constant term) / (factor of the leading coefficient)
Take the constant term. That is the last term.
Here the last term is -15. The factors of 15 are 1, 3, 5, and 15
The leading coefficient is 2, so the factors of 2 are 1 and 2

Answer 3

what else after this?

Answer 4

or is this it?

Answer 5

@Nitroster

Answer 6

@sleepyjess

Answer 7

@sleepyjess

Answer 8

theres a formula to find them i think it's p/q or something like that. I don't remember the formula. You may have it in your notes.

Answer 9

i looked it up it's all of the factors of the last term divided by all of the factors of the leading coefficient

Answer 10

so the easiest way to go about it is to right all of those possibilities and plug them into the equation if you get zero then it's a zero

Answer 11

Thank you I have been trying to get help for 3 hours had another post for the same question but no one was helping me so I took it down and made a new one I greatly appreciate your help.

Answer 12

-15: 1,3,5,15
2: 1,2

plus or minus all of these and that should be it.

Answer 13

I have a program that will give me the answer one sec so you can check your work

Answer 14

Okay thank you

Answer 15

3/2,1, and it gave me the last 2 as a decimal :(. 1.7321, -1.7321

Answer 16

so one of your fractions is going to equal 1.7321

Answer 17

take this with a grain of salt i'm not even sure anymore whether this is right or not

Answer 18

let me know if you want me to check your work

Answer 19

This whole thing is confusing ;-; honestly I don't even know right now.

Answer 20

lol i'll walk you through it

Answer 21

Thank you

Answer 22

ok so to start the formula is.
(factors of the constant)/(factors of the leading coefficient)

Answer 23

were dividing them?

Answer 24

yes

Answer 25

oh and it's plus or minus

Answer 26

okay could you set it up for me so I can do it?

Answer 27

i'll do the work but what numbers do i plug in lol

Answer 28

so we will have.....
\[\pm{1,\frac{ 1 }{ 2 },3,\frac{ 3 }{ 2 },5,\frac{ 5 }{ 2 },15,\frac{ 15 }{ 2 }}\]

Answer 29

you would plug all those numbers in to the equation if you get a zero. then the number you plugged in is a zero

Answer 30

assuming you did everything right up until I showed up everything will work just fine

Answer 31

(factors of the constant)/(factors of the leading coefficient) this formula?

Answer 32

yea

Answer 33

factors of the last term divided by the factors of theleading coefficient

Answer 34

your teacher is probably gonna want you to do synthetic or long division at this point though. This is how I do it because it's a lot faster

Answer 35

I'll try that real quick. one sec.

Answer 36

my bad i meant to say -5/2

Answer 37

which does work