Mathematics, 30.03.2021 03:40 Thomas7785
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.
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 β 1)(x β 2)
g(x) = (x + 3)(x + 2)(x β 3)
g(x) = (x + 2)(x β 2)(x β 3)
g(x) = (x + 5)(x + 2)(x β 5)
g(x) = (x + 7)(x + 1)(x β 1)
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 β a)(x β b). Describe the direction of the parabola and determine the y-intercept and zeros.
Create a graph of the polynomial function you created in Question 4.
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