Question

Hello, can someone please help me out with this? I'll fan and medal!

Answer 1

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 2

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 3

I don't want answers! I just want someone to walk me through it, step by step, and to teach me how to do it ^^

Answer 4

I can't tell if you posted this in the Physics section or not.
I'd help but I'm going to be running late for school...
@dan815 ? @amistre64 ? sorry ; ;

Answer 5

ah critical thinking skills

Answer 6

This is mathematics ^^ Algebra 2

Answer 7

well, using the fundamental thrm, what is the smallest degree polynomial we would be able to model this by using the 3 stated roots?

Answer 8

Would it be -7?

Answer 9

-7 cannot be a polynomial degree. can you post the fundamental thrm of algebra for me?

Answer 10

Any polynomial of degree "n" has "n" roots ?

Answer 11

correct, so given at least 3 roots, we should be able to form a poly of at best 3 degrees.

Answer 12

now its pretty simple to form a basic poly when we know the roots. we simply multiply all the linear root factors together.

Answer 13

f(x) = (x-r1) (x-r2) (x-r3)

the expanded form is a polynomial in x^3

Answer 14

if we wanted to get fancier, we could use multiple factors of the same root to get higher degree polynomials with the same roots. but simplicity tends to be key in these things.

Answer 15

So in this case, I'm given the points 6, -2, and -7. Instead of
f(x) = (x-r1) (x-r2) (x-r3)
Would I use, (x-6) (x,-(-2) ) and (x,-(-7) ) ?

Answer 16

correct

Answer 17

Yay!

Answer 18

http://www.wolframalpha.com/input/?i=y%3D+%28x-6%29+%28x-%28-2%29+%29%28x-%28-7%29+%29

and that actually is a fine poly that will fit the bill for us.

Answer 19

we already used the fundamental thrm to create it, so it satisfies that part by default. and now that we have the exapnded version of it, we can address the rule of sign criteria

Answer 20

This polynomial, right? y = x^3+3 x^2-40 x-84

Answer 21

And would this polynomial be used to answer the first question: "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." ? @amistre64

Answer 22

y = x^3 +3x^2 -40x -84

that would be the results yes. but you would want to show your work by expanding the product of the roots to get to that result

Answer 23

Okay ^^

Answer 24

@amistre64 Sorry its taking me a while, I have a pretty bad connection to Openstudy. It keeps on disconnecting me from the site >.<

Answer 25

the site is bad acting for us all i believe

Answer 26

your work dropped some ( ) but other than that

Answer 27

(x-6) (x+2)

x(x+2) -6(x+2)

xx+2x -6x+2(-6)

(x+7) (xx -4x -12)
^^^^^^^^
gotta wrap it for 'properness'


x(xx -4x -12) +7(xx -4x -12)

xxx -4xx -12x +7xx -4(7)x -12(7)

xxx +3xx -12x -28x -84

xxx +3xx -40x -84

Answer 28

I see ^^ XD And how about the next question?

Answer 29

" Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences. " @amistre64

Answer 30

So would I have to put the function from the first question onto the graph?

Answer 31

@amistre64

Answer 32

So I applied the equation to the graph and this came out. I don't think this is right!
@amistre64