This is the first part:
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 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Yes, Ray and Kelsey could both be correct. They could have a third degree polynomial that crosses the x-axis 3 times but the y-axis only 1 time, which would make both Ray and Kelsey right.
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.
g(x) = x3 − x2 − 4x + 4
The key features of g(x) = x3 − x2 − 4x + 4 include:
The Function Is Equal To: 0
Zeros Of This Function Are: -2, 2, and 1
Y-Intercept: 4
End Behavior: Falls to the left and goes up to the right.