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.

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zasharra · Answer

@mathmate

mathmate · Answer

Finding the x-intercepts of a general polynomial can fill a book, unless it is done strictly graphically.
Finding the x-intercepts of a quadratic or linear polynomial algebraically might fit less than a page.
Not too sure about 
"... no change in the direction of the coaster"
Is the roller-coaster in a plane or in 3-D?
If it is in a vertical plane, does "direction" mean slope?
Have you done calculus yet?
Sorry about these questions, it's because we do not know the context of your problem, nor the level of math with which you're working.

zasharra · Answer

No this is all the information they gave me. I have no clue of what they are talking about. this is everything

mathmate · Answer

If we do not have more information, I will refer you to the following link: http://tutorial.math.lamar.edu/Classes/Alg/FindingZeroesOfPolynomials.aspx http://www.purplemath.com/modules/polyends.htm http://tutorial.math.lamar.edu/Classes/Alg/GraphingPolynomials.aspx There should be sufficient information for you to solve the first part.