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## anonymous one year ago ***fan and medal***

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1. anonymous

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.

2. anonymous

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.

3. anonymous

help!!! please!!!!

4. anonymous

@ash2326 @Michele_Laino @pinkbubbles

5. Michele_Laino

a third-degree polynomial can have at maximum three zeroes

6. Michele_Laino

oops.. three real zeroes

7. anonymous

its that the answer?

8. Michele_Laino

for example, if we have the subsequent polynomial: $\Large p\left( x \right) = {x^3} - 6{x^2} + 11x - 6$

9. Michele_Laino

we can easily check that its factorization is: $\Large p\left( x \right) = \left( {x - 1} \right)\left( {x - 2} \right)\left( {x - 3} \right)$

10. Michele_Laino

which show us that there are at maximum three real zeroes

11. Michele_Laino

I think that your answer has to contain some examples

12. anonymous

someone give me the answer, you wanna check?

13. Michele_Laino

ok!

14. anonymous

Both Ray and Kelsey can both be right Ray is right because you can have 4 intercepts, three of them as zeros and one as a y intercept.

15. anonymous

its tha right?

16. Michele_Laino

an intercept is not a zero

17. anonymous

A)a third degree polynomial can have at most three x intercepts and always has one y intercept. So it can have 4 intercepts. And three zeroes . B) they are both correct because like what nightowl said about it being able to cross the x three time and the y once or depending where the exponents are either on x or y it can cross the y three times and the x once if you are looking for it crossing any and all axis (x and y) then they cross 4 times if a specific axis then it depends on the axis in shorter words the girl is only looking at one axis and the boy all

18. Michele_Laino

furthermore, the subsequent polynomial: $\Large q\left( x \right) = {x^3} - x$ has three real zeroes and it has not an y-intercept

19. anonymous

LOOK its one of them?

20. anonymous

a, or b?

21. Michele_Laino

I think that A is the correct one

22. Michele_Laino

please wait

23. anonymous

ok

24. Michele_Laino

I think option B is right, since a third-degree polynomial has three x-intercepts at maximum and only one y-intercept, so 4 intercept in total. The x-intercepts are called the zeroes of the third-degree polybomial

25. Michele_Laino

polynomial*

26. anonymous

so the answers its b, thank you so much!!!!

27. Michele_Laino

:)

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