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.
1. 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.
2. 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.
o g(x) = (x + 2)(x - 1)(x - 2)
o g(x) = (x + 3)(x + 2)(x - 3)
o g(x) = (x + 2)(x - 2)(- 3)
o g(x) = (x + 5)(x + 2)(x – 5)
o g(x) = (x + 7)(x + 1)(x - 1)
3. Create a graph of the polynomial function you selected from Question 2.