Question

Algebra II question involving polynomial equations

Answer 1

its a word problem... hold on

Answer 2

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.

Answer 3

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___

Answer 4

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.

Answer 5

Haha, very interesting. First thing we need to do is construct the polynomial from the zeroes.

Answer 6

(x-6)(x+2)(x+7) are the zeroes in a form that will create a polynomial

Answer 7

how?

Answer 8

You understand how to find zeroes by factoring, yeah?

Answer 9

yes but I don't see what equation were factoring from in this equation...

Answer 10

We are kinda reverse factoring. We are making the factors instead of getting them from an equation.

Answer 11

(x-6)(x+2)(x+7) = 0

Do you agree that if you enter any of the zeroes listed above that this equation will work?

Answer 12

wait so (x-6) (x+2) and (x+7) are the zeros? im sorry im so confused.

Answer 13

No, it's ok, there's no rush.

You're right, those are the zeroes as defined in the problem you gave.
1st point: ___6___
2nd point:___-2___
3rd point: ___-7___
are the points to use as zeroes, right?

Answer 14

yeah

Answer 15

Alright, so we can imagine it in an equation form.
If x=6, then when is this equation equal to zero, in terms of x?
x-6=0, simply by subtracting six from both sides, you see?

Answer 16

ohh okay so the answer would just be (x-6)(x+2)(x+7) = 0
and that's it? or is there more to it?

Answer 17

I believe so. if you need it in a regular form, you have to multiply it all together, but I don't see why that wouldn't work. It looks fine on my graphing calculator.

Answer 18

wait a second, actually...

Answer 19

One problem with it. Have you studied end behaviour in your class?

Answer 20

I don't think so

Answer 21

Well a cubic function usually goes towards negative infinity, as it gets negative, and goes towards positive infinity when it gets positive, so it looks like this