Question

***fan and medal***

Answer 1

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.

Answer 2

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.

Answer 3

help!!! please!!!!

Answer 4

@ash2326 @Michele_Laino @pinkbubbles

Answer 5

a third-degree polynomial can have at maximum three zeroes

Answer 6

oops.. three real zeroes

Answer 7

its that the answer?

Answer 8

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

Answer 9

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

Answer 10

which show us that there are at maximum three real zeroes

Answer 11

I think that your answer has to contain some examples

Answer 12

someone give me the answer, you wanna check?

Answer 13

ok!

Answer 14

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.

Answer 15

its tha right?

Answer 16

an intercept is not a zero

Answer 17

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

Answer 18

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

Answer 19

LOOK its one of them?

Answer 20

a, or b?

Answer 21

I think that A is the correct one

Answer 22

please wait

Answer 23

ok

Answer 24

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

Answer 25

polynomial*

Answer 26

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

Answer 27

:)