algebra

Please help!!!

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.

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asked by Legend
  1. Yes. A polynomial can have, at most, a number of zeroes equal to it's degree. A third degree polynomial can therefore have three zeroes, however, Ray is arguing that the polynomial has four INTERCEPTS. While the terms "zeroes" and "intercepts" are often used synonymously, technically a zero is an x-intercept. A function can also have a y-intercept, so in total, a cubic can have four intercepts, though only three of them will be zeroes.

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    posted by Alex
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