Option 1—Individual Roller Coaster Crew Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track. Part A The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer. Yes, there is a way for them to both be correct. The function would have three zeros, which would cross the x-axis in three places. Those would be three x-intercepts. It would also cross the y-axis which wouldn’t be a zero or a solution but it would be the fourth intercept. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros. g(x) = (x + 2)(x − 1)(x − 2) g(x) = (x + 3)(x + 2)(x − 3) g(x) = (x + 2)(x − 2)(x − 3) g(x) = (x + 5)(x + 2)(x − 5) g(x) = (x + 7)(x + 1)(x − 1) I will pick the first option End behavior: It is a positive cubic function with down-up end behavior. Y-intercept: When I graph it or when I solve it algebraically the y-intercept is (0,4) Zeros: This function has three zeros: (2,0) (1,0) and (-2,0) Create a graph of the polynomial function you selected from Question 2. Part B The second part of the new coaster is a parabola. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros. I will do f(x) = (x - 3) (x - 7). This parabola is positive and its two y-values on both of its sides go up vertically to a positive infinity value. The y-intercept is (0,21). The zeros of this function are (3,0) and (7,0) Create a graph of the polynomial function you created in Question 4. Part C Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function