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.
@mathmale can you help now?
Hi Rosie. Let's break this down a bit. Firstly, how do you find x intercepts?
I'm not sure
OH i know!
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).
If someone asked you to sketch a polynomial, what information would you want?
the x and y intercepts an the direction
but how do i find the x intercepts?
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.
Multiply your 3 factors together. This will give you a 3rd order poly that looks like ax^3 + bx^2 + cx + d.
so how about x^3 - 4x^2 - 11x + 30
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.
RosieF Human Calculator Best Response Medals 0 but how do i find the x intercepts? You invent them (for this particular question).
Good luck, Rose. I have to get off the 'Net for the time being. Happy to work with you.
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?