OpenStudy (anonymous):

PLEASE PLEASE HELP!!!!!! 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 of degree 3 or higher to use in your explanations.

OpenStudy (anonymous):

@mathmale can you help now?

OpenStudy (anonymous):

Hi Rosie. Let's break this down a bit. Firstly, how do you find x intercepts?

OpenStudy (anonymous):

I'm not sure

OpenStudy (vickyisthesmartone123):

OH i know!

OpenStudy (anonymous):

x intercepts are the points where R(x) intercepts the x axis, so when y=0. The x intercepts occur at x values satisfying R(x)=0. Finding these x values can be done by factoring, iteration or just with one of the formulas for the degree of polynomial (up to a limit).

OpenStudy (anonymous):

If someone asked you to sketch a polynomial, what information would you want?

OpenStudy (anonymous):

the x and y intercepts an the direction

OpenStudy (anonymous):

@tom982

OpenStudy (anonymous):

but how do i find the x intercepts?

OpenStudy (mathmale):

This is a challenging question. You are invited to invent your own zeros. Since you're to use a 3rd order equati9on to describe the motion, choose any 3 points on the x-axis. If, for example, you choose x=2, then one factor of your 3rd degree polynomial will be (x-2). Create 2 more factors.

OpenStudy (mathmale):

Multiply your 3 factors together. This will give you a 3rd order poly that looks like ax^3 + bx^2 + cx + d.

OpenStudy (anonymous):

so how about x^3 - 4x^2 - 11x + 30

OpenStudy (mathmale):

Now for the rest of the question: "so that the engineer can predict when there will be no change in the direction of the coaster" I have trouble with this. The roller coaster is constantly changing direction. Perhaps you or someone else could provide an explanation of what is sought here.

OpenStudy (mathmale):

RosieF Human Calculator Best Response Medals 0 but how do i find the x intercepts? You invent them (for this particular question).

OpenStudy (mathmale):

Good luck, Rose. I have to get off the 'Net for the time being. Happy to work with you.

OpenStudy (anonymous):

okay thanks

OpenStudy (anonymous):

Hi Rosie sorry I was helping someone else. \(x^3 - 4x^2 - 11x + 30=0\) is perfect. We know the x intercepts of this are \(-3\), \(2\) and \(5\). What is the y intercept of this function?