Question

I really need help with my Algebra 2 polynomial equation work. Someone please help me im begging!

Answer 1

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.

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 rollercoaster. 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 rollercoaster. If your y–intercept is off the graph, give the coordinates of the y–intercept.

Answer 2

thats everything someone please guide me through it and teach it to me i would love that

Answer 3

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 rollercoaster. Show all of your work.

First, think of "the foundation" as being the x-axis. In other wordsd, the roller coaster touches the x- axis at -7, at -2 and at 6, but does not go beneath the x-axis.

Thus, you automatically have three on the curve formed by the roller coaster.

Are you aware that a root of 6 corresponds to the factor (6,0) of the polynomial in question?

What are the other two factors, following this pattern?

You can obtain the polynomial in question by multiplying out the three factors mentioned. Try this, and then get back here to request some feedback. Good luck!!

Answer 4

what? i am so confused @mathmale

Answer 5

so if i have (6,0) and (-2,0) and (-7,0) what do i do

Answer 6

@mathmale how do i make a polynomial function with those

Answer 7

(6,0) and (-2,0) and (-7,0) are points on the x-axis; they're not factors.
what I was trying to tell you was that if one root is 6, one factor is (x-6); if another root is -2, the corresponding factor is (x-[-2]). What is the third factor?

To get started finding your polynomial, please multiply together (x-6) and (x+2).

Answer 8

the third factor is (x-(-7) @mathmale

Answer 9

and ill get x^2-4x-12 @mathmale

Answer 10

Right. So, now you have three horiz. intercepts, (6,0) and (-2,0) and (-7,0) , and you have three factors, (x-6),(x+2) and (x+7).

Now, with x^2-4x-12 in hand, multiply this polynomial by the third factor, (x+7). Combine like terms. Write your function so that all powers of x are in descending order.

Then you'll have your polynomial.

Answer 11

x^3+x^2-28x-12x-84 @mathmale

Answer 12

@mathmale What do i do now? the next step i REALLY dont get at all

Answer 13

Your function / your polynomial is f(x)=x^3 + x^2 -28x -12x - 84 . Nice work!

Answer 14

@mathmale but what about the next part

Answer 15

MATHMALE IS GOOD. GIVE HIM A MEDAL. :D

Answer 16

@DavidUsa I was planning on it when we were done

Answer 17

yay :):D

Answer 18

Second part: " Using both fundamental Theorem and Descartes` rule of signs, prove to the construction foreman that your funtion matches your graph. Use complete sentences." I have to admit that I don't remember the details of either the Theorem or Descartes' Rule of Signs. However, thanks to the Internet, it'd be a simple matter to look them up. I'd suggest you start by Googling Descartes' Rule of Signs; by doing that you'd have an excellent chance of finding an explanation with examples of this rule.

the whole idea is to determine whether or not the graph crosses the x-axis or not. In our case, here, we'd hope that the Rule of Signs would predict that the graph does not cross the x-axis. But don't take my word for it; please research this in your textbook or through a Google search.

Answer 19

can i use an actual graphing program to see if it does @mathmale

Answer 20

Certainly! that won't satisfy the requirement that you use both of the two methods named to arrive at your answer, but the more you know about the shape of the graph, and whether or not it touches / crosses the x-axis, the better!

Answer 21

@mathmale can you help me with question 3

Answer 22

ummm.... just saying.... u dont have to write @mathmale. @davidusa. @blah. everytime

Answer 23

Princess: I used wolframalpha.com to graph your function:

http://www.wolframalpha.com/input/?i=f%28x%29%3Dx%5E3+%2B+x%5E2+-28x+-12x+-+84

Unfortunately, wolframalpha shows that the graph of your function DOES cross the x-axis. This means we'll need to go back and double-check the multiplication of those three factors.

Answer 24

so what do we do if it's all right?

Answer 25

like what do we need to change

Answer 26

@mathmale

Answer 27

Hold a moment, please.

Don't worry, I'm sticking with you and this conversation.

One thing you could do would be to copy down your 3 factors and multiply them together again, in different order, and then compare the result to your original f(x).

Answer 28

ok one second im doing it now

Answer 29

Aha. Reading the problem statement again, I see mention of "a map of current structures." Was there an illustration with this problem? If so, would you please post it?

Answer 30

the map is the picture i posted

Answer 31

If these structures have their floors / foundations at different levels, then it's entirely possible that our polynomial is just fine, and that the graph DOES cross the x-axis.

Answer 32

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.

Answer 33

this is at the very begging

Answer 34

Aw, shoot. Your illustration shows that all of the structures have their foundations at the same level, so that means my hypothesis is shot.

" plummet underground, pop back up, and coast over a hill before shooting back underground" uh-oh. So the path of the roller coaster DOES cross the x-axis. Proof, beloved proof!

So let's go back and take a look at the graph we got courtesy of wolframalpha.com.

Answer 35

so does that mean the polynomial is fine or do i need another one

Answer 36

because i have another one if you need one

Answer 37

mousy

Answer 38

Have a look at

http://www.wolframalpha.com/input/?i=f%28x%29%3D%28x-6%29%28x%2B2%29%28x%2B7%29

Answer 39

@mathslover What does the graph mean

Answer 40

omg does it go around the figures

Answer 41

Look at the first part of your problem statement:

"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."

Then look at the graph (courtesy of wolframalpha.com): At how many places does this graph cross the x-axis?

Answer 42

the graph does that!

Answer 43

Yes, it crosses the x-axis in 3 places. So, it appears that we're right on target.

Answer 44

so is that it?

Answer 45

No. Read the last part of the problem statement and type, in your own words, what we still have left to do.

Answer 46

how do i solve for the y inercept

Answer 47

oh ok :)

Answer 48

Suppose I gave you f(x)=x^2 -x -3. How would you find the y-intercept of the graph of this function?

Answer 49

plug in numbers for x

Answer 50

What number(s) would you plug in?

Answer 51

i have no idea ahaha

Answer 52

What does "y-intercept" mean to you?

Answer 53

Important concept, especially in graphing.

Answer 54

the vertical up and down line

Answer 55

that's the y-axis. Our task is to determine where the graph crosses the y-axis.
Plese look at the graph again:

http://www.wolframalpha.com/input/?i=f%28x%29%3D%28x-6%29%28x%2B2%29%28x%2B7%29

Estimate the y-value where the graph crosses the y-axis.

Answer 56

it crosses the y axis at 0,0

Answer 57

oh wait wrong graph

Answer 58

(0,0) is the origin; I see that the graph crosses the y-axis below the origin (so that the y-value in question is negative).

Answer 59

so did we find the y

Answer 60

Not yet. Have you looked at the graph by wolframalpha.com?

http://www.wolframalpha.com/input/?i=f%28x%29%3D%28x-6%29%28x%2B2%29%28x%2B7%29

Look at it again, and then estimate the y-value where the curve crosses the y-axis.

Answer 61

which graph am i supposed to look at the first of second one

Answer 62

is it (-5,0)

Answer 63

the first scale division is -200, right? So, does it sound right when I suggest that the curve crosses the y-axis at about -80?

Answer 64

When writing the y-intercept, Princess, you'd want to write it as (0, Y) (0 first, Y second).

Answer 65

oh! omg i was looking at the x axis for some reason

Answer 66

so its (0,-80)

Answer 67

Approx.

Just a sec, please.

Answer 68

ok

Answer 69

the function you came up with is f(x)=x^3 + x^2 -28x -12x - 84.

Would you now please let x=0 and calculate y=f(0).

Answer 70

so everywhere that there is an x i put 0

Answer 71

Right on.

Answer 72

f(x)=84

Answer 73

Actually, it'd be f(0) = -84, wouldn't it?

Answer 74

yes!

Answer 75

So, by letting x=0, you have arrived at f(0)=-84; this point can be written as (0,-84). By what name shall we call this point? (I'm always trying to review stuff!).

Answer 76

the y intercept?

Answer 77

Right! And although you still have to respond to the request for verbal explanations in this problem statement, you're essentially done with the number-crunching (math) part. :)

Answer 78

so i would basically say that i put 0's in for all of the x's and then do the math

Answer 79

True ... but I'm afraid you'll also have to explain other parts of the problem solution as well. Don't want to ruin your evening! But that's what the problem asks for.

Answer 80

youre not ruining my evening haha but do you mean that i explain the rest of what i did

Answer 81

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

Answer 82

oooooh ok

Answer 83

i looked those up and i still dont understand them

Answer 84

Best to you, Princess. Do call on me again in the future. Good night!

Answer 85

ok and thank you for everything :)

Answer 86

I won't be able to go into those right now, but perhaps if you could catch me online tomorrow, we could look them up together and discuss them. Have you a textbook for this course, a real, paper textbook?

Answer 87

nope becuase i am doing virtual school

Answer 88

MATHMALE IS HELPFUL HE DESERVES A FAN FOR HIS HARD WORK :D

Answer 89

david im not trying to be mean but why are you still here?

Answer 90

im talking to mathmale and watching him do magic

Answer 91

I meant: Your being a virtual school student ... that poses a REAL challenge. As I'm deaf, it's hard for me to conceive of learning math without textbooks. As an online student you have to develop skills not only in learning stuff but also in finding it first online. I hope we can meet tomorrow to discuss this further.

Answer 92

i love being an online student :) I have straight A's

Answer 93

omg your deaf ive never met a deaf person!

Answer 94

that's fantastic, Princess!!

Answer 95

youre so cool!

Answer 96

I do get a kick out of helping others online, not intentionallyl concealing the fact that I'm deaf, but realizing that my being deaf does not in any way lessen my ability to help with Math.