Question

The shape of a roller coaster is modeled by a polynomial function, R(x). Describe how to find the x-intercepts of R(x) and how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster. You may create a sample polynomial of degree 3 or higher to use in your explanations.

Answer 1

Polynomial Equation: R(x)=4x^3+2x^2-7
Degree: 3
We then Plug in 1.059 in as X so it would look like
R(1.059)=4(1.059)^3+2(1.059)^2-7
This then Equals R=-0.00608544
^what i have so far

Answer 2

@Mehek

Answer 3

You will need three roots for this, so we have

 Let x = -30, -10 and
+20

So the factors will be  (x+30)(x+10)(x-20)

The divide it to 100, this will help bring the peak up and
down

So the polynomial function R(x) will become

1/100 * 
(x+30)(x+10)(x-20)

R(x) = 1/100 * (x+30)(x+10)(x-20)

 

Finding the X-intercept:

Let R(x) = 0 and solve for x.

1/100 * (x+30)(x+10)(x-20) = 0

x = -30, -10, 20 are the x-intercepts.

Answer 4

-.- i dun want copy and pasted answers i need actual help

Answer 5

You find x-intercepts by first factoring then solving for x

Answer 6

and if you can't factor you use the quadratic formula

Answer 7

Wait ok so whatt and how am i factoring

Answer 8

Factoring 4x^3 + 2x^2 - 7

Answer 9

ok hold on let me do it e.e

Answer 10

I dont think you can factor this

Answer 11

Right so then you use the quadratic formula

Answer 12

if i did it correctly it would be x=1.059 which i added as X

Answer 13

Polynomial Equation: R(x)=4x^3+2x^2-7
Degree: 3
I Tried to factor 4x^3+2x^2-7 but it didnt work so i used the quadratic formula which equaled x=1.059 which we Plug in 1.059 in as X and made y zero so it would look like
R(1.059)=4(1.059)^3+2(1.059)^2-7

Answer 14

\(\bf{x=\dfrac{-b±\sqrt{b^2-4ac}}{2a}}\)

Answer 15

huh?

Answer 16

That's the quadratic formula

Answer 17

a is the coefficient of the first term, b is the second, c is the third

Answer 18

......

Answer 19

i thought i already solved it i said it was 1.059 am i wrong?

Answer 20

\(\bf4x^3+2x^2-7\) where

a = 4
b = 2
c = -7

Answer 21

oop i didn't see the reply

Answer 22

so i am right ?

Answer 23

Yes

Answer 24

So that's where the graph intercept the x-axis

Answer 25

wait whats next? if the equation looks like this what do i do?
R(1.059)=4(1.059)^3+2(1.059)^2-7

Answer 26

That gives you the point for the x-intercept
(1.059, R(1.059))

Answer 27

Since you found what x is equal to you don't need to plug it in because that's all you do for the x-intercept

Answer 28

Polynomial Equation: R(x)=4x^3+2x^2-7
Degree: 3
I Tried to factor 4x^3+2x^2-7 but it didnt work so i used the quadratic formula which equaled x=1.059
This then gives use the point for the x-intercept
(1.059, R(1.059))
^is that all i have to do?

Answer 29

You can put (1.059, 0) cause it's the same thing

Answer 30

And yes that's all

Answer 31

For the first part

Answer 32

First part? what else do we have to do?

Answer 33

"Describe how to find the x-intercepts of R(x) and `how to construct a rough graph of R(x) so that the engineer can predict when there will be no change in the direction of the coaster`."

Answer 34

would it look like this?

Answer 35

Yeah but you have to say how you can construct it
So first you'd plot the x-intercept
Then you'd find the y-intercept which is plugging all the x with 0 and getting -7 so you'd plot (0,-7)

Answer 36

Have you learned how to find the minimum/maximum of a graph?

Answer 37

wait ok hold up so
That way you can construct this graph is to first plot the x intercept which is 1.059 then you find the y intercept which is -7 because you plug everything in x with 0 which gives you -7 this would make your graph Decrease and go down.

Answer 38

Ummmm i probably did but forgot e.e

Answer 39

Correct

Answer 40

so would that be the answer for part 2

Answer 41

to find min/max

\(\bf x= \dfrac{-b}{2a}\)

Answer 42

Yeah it would but it also mentions changes in direction so idk if you need the min/max

Answer 43

It changes direction as it decreases would that work

Answer 44

Yeah ig that works

Answer 45

Thank you would you possibly be able to help me with a few more e.e

Answer 46

ill make sure yew get lots of medals >.<

Answer 47

Gee I still helped 😒😒