Question

Will fan and medal please :)
Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.

Answer 1

Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
No because polynomials cannot have anything that equals zero. Polynomial functions have to equal a number bigger than zero.


Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros. choice
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14

The end behavior of this g(x) function is a positive 4. The y-intercept of this function is


Create a graph of the polynomial function you selected from Question 2.


Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.


The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.


Create a graph of the polynomial function you created in Question 4.


Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.


Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.

Answer 2

i answered Part A but i have no idea if im doing this right?

Answer 3

@escamer @ddaum03

Answer 4

@skatergirl147 @rarecigs

Answer 5

@jovanny21 can u help?

Answer 6

@drawwithapurpose

Answer 7

@jr1998789

Answer 8

@thalya_15

Answer 9

@Trevor12

Answer 10

https://www.desmos.com/calculator this might help with the rest of your questions but i don't understand part c.

Answer 11

how can i get a moderater?

Answer 12

a moderator? well...you just tag them like any other person

Answer 13

like @mathmale

Answer 14

can u help with that?

Answer 15

he's a mod

Answer 16

and we wait?

Answer 17

mhm or ask different mods like @tkhunny

Answer 18

how do i know whos a mod and whos not?

Answer 19

mods are the people with purple usernames and purple boxes around their profile pictures.

Answer 20

@SeanStewart16 help?

Answer 21

you can also try @perl . perl is a qualified helper and a mod...so she might help

Answer 22

@NetflixAndNo

Answer 23

@Awolflover1

Answer 24

@alibaby

Answer 25

@jesus14

Answer 26

yes? im so confused what do u need help in

Answer 27

algebra 1

Answer 28

all of this

Answer 29

@PicklePlanet

Answer 30

help?

Answer 31

i know a moderator, want me to call him?

Answer 32

i need help with this

Answer 33

ill call him

Answer 34

yea man this is pretty hard

Answer 35

Can someone help?

Answer 36

@mathmale

Answer 37

tagged him already he hasnt come yet

Answer 38

dude, what class is this for?

Answer 39

Algebra 1

Answer 40

@Awolflover1 @hartnn @hacker89 @HarleyQuinn98 @Kitten_is_back @ParthKohli @Safa102 @SamsungFanBoy @TheCuteOne25 @YoungStudier @you_me @Zeronknight

Answer 41

@mathmale

Answer 42

hes coming, he just noted me

Answer 43

First, I need to know where you (Hunter68) currently are in your approach to this problem. Your post covers a lot of material. What specifically do you need to learn and do?

Answer 44

i need help with all of it
@mathmale and i am in the middle of A

Answer 45

i have no idea if i am doing this right...

Answer 46

"No because polynomials cannot have anything that equals zero. Polynomial functions have to equal a number bigger than zero." I can't agree to either response.

First of all, we routinely set polynomials = to zero when the goal is to find roots / solutions / zeros. Secondly, polynomials can have both positive and negative values, as well as zero.

I'd suggest you find a couple of third degree polynomials and graph them before you try to answer Part A.

Answer 47

I've just given you some feedback. See my previous message.
Are you learning from a textbook? Do you have printed study materials? If no, what is your primary source of info on Algebra I?

Answer 48

I am homeschooled

Answer 49

with FLVS

Answer 50

So, if you were looking up "polynomials," or "graphing polynomials," where would you go?
I'm glad for the opportunity to help you with this problem, but do not feel it'd be appropriate to start from scratch explaining this material. That's why I ask you to formulate specific questions that we can discuss.

Answer 51

I use Desmos or Google or this

Answer 52

Have you Googled "graphs of third-order polynomials?"

Answer 53

I googled can 3rd order polynomials have zeros and got that

Answer 54

That's entirely true, but not enough info.

I looked up "third order polynomials" and obtained the following results:

https://www.google.com/search?sourceid=chrome-psyapi2&ion=1&espv=2&es_th=1&ie=UTF-8&q=third-order%20polynomials&oq=third-order%20polynomials&aqs=chrome..69i57j0l5.3763j0j7

The reason I'm asking you to do some research here is that you'd benefit from seeing examples of the graphs of third-order polynomials.

Can you use the Draw utility to sketch y=x^3?

Answer 55

what do u mean by sketch? and draw utility?

Answer 56

I've just demonstrated it by typing / drawing y = x ^3
and by setting up a system of coordinate axes (x- and y-axes).

Answer 57

Please have a look at

http://www.sscc.edu/home/jdavidso/Math/Catalog/Polynomials/Third/Third.html

because this site features graphs of a couple of third-order polynomials. It's essential that y ou know what such polynomials look like.

Answer 58

You could edit my graph by clicking on the pencil icon in the upper, right hand corner of the graph. A new graph in a different color will open. You can type or draw on that graph. Graph y=x^3.

Answer 59

im more confused than ever

Answer 60

Please look up this web page. Do you see examples of graphs of 3rd order polynomials there?

Answer 61

http://www.sscc.edu/home/jdavidso/Math/Catalog/Polynomials/Third/Third.html

Answer 62

nvm im going to see if Ms.Roessler can help...(my teacher) i am sorry for the inconvenience but your just confusing me more

Answer 63

All right. Sorry that our interaction is not working out.

Answer 64

its ok openstudy is awesome :)

Answer 65

It may sound old-fashioned, but asking Ms. Hunter about a good algebra book that you could purchase and study might be one of the best things you could do to help yourself.
Back in my day (1944) there was no such thing as an "Internet" or "OpenStudy," and so everything I learned came from books. Just a thought. I get the impression that you need more background in algebra than you currently have, to do the problem you've shared here on OpenStudy. Good luck, Hunter. Let me know what you learn from Ms. Hunter.

Answer 66

Ms.Roessler* and please call me Ray and thanks

Answer 67

OK. Hope Ms. R. can help you; sometimes it's best to have a live teacher who gets you involved. Take care, Ray. Bye. Over and out.

Answer 68

bye

Answer 69

ok now i need help with part C and D

Answer 70

@SeanStewart16

Answer 71

@ilovebmth1234