Question

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

Hints:
Intercepts could mean either x-intercept or y-intercept.
3 zeroes means three x-intercepts.

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.