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 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 − 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)

Create a graph of the polynomial function you selected from Question 2.

Answer 1

From the information given about the polynomial function, It is correct to state that there is a way for both of them to be correct. See the explanation below and the attached for the graph related to the second question.

What is the explanation for the above?

A polynomial could only have a number of zeros equal to its degree. A third degree polynomial can thus have three zeroes, but Ray claims the polynomial has four Intercepts.

While the words "zeroes" and "intercepts" are sometimes used interchangeably, a zero is officially an x-intercept. A function can also have a y-intercept, therefore a cubic can have four intercepts in total, albeit only three will be zeroes.

The zeros of g(x)= x3-x2-4x+4 are -2,2, and 1. End behavior, the Y- intercept, the axis of symmetry, and the vertex are other important characteristics of polynomial functions.

Learn more about polynomial functions at;
brainly.com/question/2833285
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