Question

Hello! Can someone help me with my problem? First, here is the existing map of current structures. It is important that the roller coaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your roller coaster. Show all of your work.
Thanks

Answer 1

tag jigglypuff314

Answer 2

@jigglypuff314 can you help me with my problem?

Answer 3

he can help

Answer 4

*scratches head* I'm not too sure how to explain it
it's like... for example an equation like (x-2)(x+3)(x-5)
would give the zeros -3, 2, 5

Answer 5

Okay, but how would I create a function out of that? Maybe it would help if I gave you the entire question?

Answer 6

yes, that would help :)

Answer 7

As one of the new roller coaster engineers, you have been tasked with developing a roller coaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the roller coaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground. There must be three distinct points where the roller coaster crosses the x–axis. Precise measurements and attention to detail are very important.
coordinate plane with buildings blocking off x–intercepts of negative 11, negative 10, 0, 1, 2, 3, 9, and 10

First, here is the existing map of current structures. It is important that the roller coaster does not go through the foundation of any of these structures.

1st point: ___6___
2nd point:___-2___
3rd point: ___-7___

Using the points above as zeros, construct the polynomial function, f(x), that will be the path of your roller coaster. Show all of your work.



Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences.



Solve for the y–intercept for your function, f(x), and then construct a rough graph of your roller coaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.

Answer 8

right... ummm I can try (but I failed algebra 2)
all I know is that if you want the zeroes to be -7, -2, 6
then (x-(#))(x-(#))(x-(#)) = f(x) would get you that...

Answer 9

So, it would be like f(x) = (x-7)(x-2)(x+6)? Then I would use FOIL to eliminate the first two factors? I'm slightly confused.

Answer 10

close, it would be like (x+7)(x+2)(x-6)

Answer 11

okay. then I would have something like this for my next step: then what would I do to finish my equation?

Answer 12

you don't really have to (I think)
but if you want....
after (x^2 + 9x + 14)(x-6) is
(x^2)(x) - (x^2)(6) + (9x)(x) - (9x)(6) + (14)(x) - (14)(6)

Answer 13

o_O? I am confused by your equation?

Answer 14

it's distrbutive
(x^2 + 9x + 14)(x-6)
is like x(x^2 + 9x + 14) - 6(x^2 + 9x + 14)

Answer 15

would you then solve and multiply x and -6 (respectively?)

Answer 16

mmm? you would distribute the x through (x^2 + 9x + 14)
and then the (-6) through (x^2 + 9x + 14)
and get (x^2)(x) - (x^2)(6) + (9x)(x) - (9x)(6) + (14)(x) - (14)(6)

Answer 17

\[x^3 - 6x^2 + 9x^2 - 54x + 14x - 84\]

Answer 18

Then I would simplify and combine like terms?

Answer 19

yes :)

Answer 20

which would be:
\[x^3 + 3x^2 - 40x - 84\]

Answer 21

yup :)

Answer 22

then what would I do from there?

Answer 23

I think f(x) x^3 + 3x^2 - 40x - 84
would just be the answer for that part?