Question

Please help! Been stuck on this question.
The shape of a rollercoaster 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 to be used in your explanations.

Answer 1

May be like this. Make a quadratic polynomial and then find the d/dx it shall give the tangent to the curve. And at point where the equation is zero will be the turning point. May be like this... @loser66 may help you with this and correct my follies.

Answer 2

So could I create a polynomal like x^2 - a^2 = (x+a)(x+a)

Answer 3

Oh no wait, it has to be R(x)

Answer 4

make a parabolic function like 2x^2+5X+6

Answer 5

So R(X) = 2x^2 + 5x +6

Answer 6

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeF4yKzV4KzYiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItOC4wNTk5OTk5OTk5OTk5OTkiLCI0Ljk0IiwiLTAuMjc5OTk5OTk5OTk5OTk5NiIsIjcuNzIwMDAwMDAwMDAwMDAxIl19XQ--

Answer 7

are you able to follow the link ?

Answer 8

Yes, it shows the graph of the function

Answer 9

Wont, this parabolic function be a analogy of a roller coaster.

Answer 10

Yeah, it's like a "sample" you have to create one and describe how to find the x-intcepts and how to construct a rough graph

Answer 11

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiIyeF4yKzV4LTYiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDAsIndpbmRvdyI6WyItOS4yIiwiMy44MDAwMDAwMDAwMDAwMDA3IiwiLTIuODU5OTk5OTk5OTk5OTk5NCIsIjUuMTQwMDAwMDAwMDAwMDAxIl19XQ--

In this equation there is 2 x intercepts. or turning point. Just think about this and say

Answer 12

BUt how do I find the x-intercepts without looking at a graph

Answer 13

can you find the roots of a parabola..?

Answer 14

No not really :/ this lesson was pretty hard for me to understand

Answer 15

Say me one thing you need to make a general equation or just a defined equation, where the variables are placed.

Answer 16

I need to explain how to solve the findings of the x-intercept

Answer 17

I am explaining you again from the initials ok with a different example, a general example. ok

Answer 18

Okay

Answer 19

Take the equation to be

ax^2+bx+c

which is the equation of a parabola.

following ?

Answer 20

Yes, i'm writing it along on a piece of paper

Answer 21

now this quadratic equation could be solved if \[x=(-b \pm \sqrt{b^2-4ac})\div2a\]

if you now have any equation and put the variable according to this you will find the roots of the equation. i.e. the point where the function will have 0 value and those points shall be your turning point or you call the x intercepts.