20
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.

You will need three roots for this, so we have
Let x = -30, -10 and +20
So the factors will be (x+30)(x+10)(x-20)
The divide it to 100, this will help bring the peak up and down
So the polynomial function R(x) will become
1/100 * (x+30)(x+10)(x-20)
R(x) = 1/100 * (x+30)(x+10)(x-20)

Finding the X-intercept:
Let R(x) = 0 and solve for x.
1/100 * (x+30)(x+10)(x-20) = 0
x = -30, -10, 20 are the x-intercepts.