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.
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If the polynomial function representing the roller coaster was R(x) = x^3 - 4x^2 - 11x + 30, you can find the x-intercepts by factoring the equation. After factoring, you find that of R(x) = (x - 5)(x - 2)(x + 3). You then make three separate equations in which each factor is equal to zero and solve for x. The result of those equations will be x = 5, x = 2, and x = -3. Therefore, the x-intercepts for R(x) will be x = 5, x = 2, and x = -3. You can now graph the function by first placing all 3 x-intercepts. Then, you can roughly draw the behavior of the graph by having it go up past (-3, 0), down past (2, 0), and back up again past (5, 0). ?