Question

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 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.

Answer 1

A 3rd degree polynomial can have as many as 3 roots or x intercepts, we can show that by graphing a function y=x^3-3x^2+3



a nth degreee polyynomial can have as many as n x intercepts

but, ray can be right if he is talking about x and y intercepts, but probalby not because that would be when x=0 or when the ride starts



they can both be correct if ray is talking about x and y intercept
and kelsey is corect because zeroes are x intercepts only

Answer 2

Answer:

In general terms, an nth degree polynomial has n zeros, for example, a first-degree polynomial (a line) has 1 zero. Then a third-degree polynomial function  has 3 zeros, as Kelsey said. But Ray said the function has 4 intercepts, which are the 3 zeros (interceptions with the x-axis) and the y-intercept (every polynomial has 1 y-intercept), so he is also correct.