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.

Question

Mathematics

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1 January, 19:19

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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Answers (2)

Know the Answer?

Rowan Jones · Answer 1

Hints:

Intercepts could mean either x-intercept or y-intercept.

3 zeroes means three x-intercepts.

Daphne Pena · Answer 2

Sure there is.

The function has three zeros ... it crosses the x-axis in 3 places.

Those are three x-intercepts.

It also crosses the y-axis. That's not a 'zero' or solution,

but it's the fourth intercept.

I slapped together a "third-degree polynomial function" in a hurry

that I think does the job. I'm not positive ... you should check it:

f (x) = x³ + 6x² + 11x + 6

==> f (x) is zero when x = - 3 or - 2 or - 1 ... those are three x-intercepts.

==> f (x) is 6 when x = 0 ... that's the y-intercept.

I don't know what "the first pattern in the coaster plan" means.