Question

Medal and I'll fan you!
Using those points as zeros, construct the polynomial function, f(x) that will be the path of your roller coaster. Show all of your work. That's the question and i made these my points :
1st point: (-11,8)
2nd point: (-5,-4)
3rd point : (7,7)

Answer 1

How did you generate these points, and if they are zeros of the polynomial, then why is the y-coordinate for each not zero?

Do you anticipate that the polynomial function will be a quadratic?

Answer 2

It just asked to pick 3 points that didn't have the buildings on them.

Answer 3

I don't understand this: Using those points as zeros, ...

The points listed are not zeros.

Maybe you could post the diagram.

Answer 4

okay one second :)

Answer 5

@Directrix

Answer 6

Where are the instructions you were given about choosing 3 points that are zeros of the polynomial?

These are not zeros.

1st point: (-11,8) 2nd point: (-5,-4) 3rd point : (7,7)

It is correct that they do not have buildings on them.

Answer 7

What about three points such as:

(11,0)
(5,0)
(-8,0)

Answer 8

Is this the question:

As one of the new rollercoaster engineers, you have been tasked with developing a rollercoaster that will intertwine with existing Oakville Lake Amusement Park structures. For one of the more thrilling sections, the rollercoaster 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 rollercoaster crosses the x–axis. Precise measurements and attention to detail are very important.

First, here is the existing map of current structures. It is important that the rollercoaster does not go through the foundation of any of these structures. Pick three points on the x–axis that the rollercoaster will dive underground or resurface. (Points that have a building on them are off-limits.)
1.The rollercoaster will run from right to left, so work in that order when selecting points. •1st point:______
•2nd point:______
•3rd point:______

Answer 9

YES!

Answer 10

@Hannah28

Read through this (same problem plus solution) and see what you think.

http://openstudy.com/study#/updates/526a9861e4b08ed552540a02

I'll read it, too.

Answer 11

I read through that and I'm not 100% sure what to do still but I think I might have an idea...

Answer 12

Definitely, change those points so that they are zeros of the polynomial.

Answer 13

so choose points on the x line?

Answer 14

The rollercoaster will run from right to left

So the points should go in descending order.

Answer 15

7, 4, -12?

Answer 16

Did you see this: the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground.

Answer 17

Oh my gosh :( I didn't even see that!

Answer 18

they used 5, -4, -12 so is there only one answer or could I use different points?

Answer 19

I think there will be different answers based on the zeros you choose.

Use different points. Then, we will crank out the polynomial, draw its graph, and see if it goes under anything.

These points you had at the start:

7, -5, -11 --> Do they run into any of the buildings?

Answer 20

-11 does

Answer 21

-11 does

Answer 22

so could I change that to -12?

Answer 23

Now, I'm thinking that the points have to be chosen to make the RC do this: the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground.

Answer 24

will these points do that?

Answer 25

It may be doing this. What do you think?

Answer 26

Is that what I want?

Answer 27

I don't know. I just went by this: the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground.

Answer 28

Now, what are the points that would go with that diagram?

Answer 29

(5,0); (-4,)); (-13,0)

Answer 30

5 -4 -13?

Answer 31

Yup!:)

Answer 32

Let's try:

y = (x -5)*(x+4)*(x+13)

Oh,no.

Look at the graph here:

http://www.wolframalpha.com/input
/?i=y+%3D+%28x+-5%29*%28x%2B4%29*%28x%2B13%29


It is not doing this: shooting back underground.

Answer 33

how is that not right? It looked like we want it to?

Answer 34

I was going by this: The rollercoaster will run from right to left.

Now, I cannot find where I read it in the original problem.

Answer 35

it is coming down from right though

Answer 36

But, the RC does not pop back up at x = -13

Answer 37

is it supposed to?

Answer 38

it looks like the diagram you made?

Answer 39

I think I have forgotten how to read:

See if the RC graph is doing this:


the rollercoaster will dive down in-between buildings, plummet underground, pop back up, and coast over a hill before shooting back underground.

Answer 40

that's what its doing :)

Answer 41

We should check to see if the RC crashes into any of the three buildings.

Answer 42

oh that's smart

Answer 43

How do I know if it crashes or not?

Answer 44

You could evaluate y = (x-5)(x+4)(x+3) for x = 1.5, x = 9.5, and x = -10 to determine if the y values for each of those is higher than the buildings.

Or, we could put a factor of 10 in front of the polynomial to make it taller. Let's see what that looks like.

Answer 45

Those look like they work to me :)

Answer 46

The multiplication by 10 may take the FW into outer space. I don't know.

Answer 47

Oh :( I'm really confused!

Answer 48

We can go with the original:

y = (x -5)*(x+4)*(x+13)

which as a polynomial is:

P(x) = x³ + 12 x² - 33x - 260

Answer 49

how did you get that equation?

Answer 50

www.wolframalpha.com is your friend.

Click on this link:

http://www.wolframalpha.com/input/?i=y+%3D+%28x+-5%29*%28x%2B4%29*%28x%2B13%29

Answer 51

You can multiply those binomials by hand to check.

Answer 52

Im lost...

Answer 53

You asked this: how did you get that equation?

I multiplied this y = (x -5)*(x+4)*(x+13) out to be in polynomial form.

If 5 is a zero of the polynomial, then (x-5) is a factor of the polynomial.

If -4 is a zero of the polynomial, the (x- (-4)) = (x + 4) is a factor of the polynomial.

If -13 is a zero of the polynomial, then (x - (-13)) = (x+13) is a factor of the polynomial.

So, the entire polynomial is the product of those three factors: (x -5)*(x+4)*(x+13).

I used an online calculator to multiply all that.

You can check that multiplication if you like by multiplying it out with paper and pen/pencil.

Answer 54

@Hannah28 Does this ^^^ make sense?

Answer 55

I left for the beach sorry :( Thank you @Directrix