A Roller Coaster to die for

Roller Coaster Design

By:

Dannielle Franco

and

Aeriane Crisostomo

(Grade 10 – Honesty)

Let’s face it, making a roller coaster design is not easy. You can not just make one without considering facts. Great roller coaster designs needs ‘The Brains’ not just imagination and your hunger for excitement. Now, let’s talk about “the Brain” that makes this awesome structure come alive!

In making roller coaster designs, we need a concrete idea of what we are doing. We need polynomial functions. I know you might say, “What does a polynomial function got to do with a roller coaster?!” the answer is simple. Polynomial functions can be graphed that will resemble a perfect roller coaster. With its turning points and death-defying heights when put into structure, our polynomial function can turn into a roller coaster that will take your breath away. How do we do it?

Here’s how....

Function:

P(x) = x6 – 7x5 + 7x4 + 35x3 – 56x2 – 28x +48

First we need a polynomial function that we can graph into a roller coaster to die for.
A. End Behavior The leading coeffiecient is positive and its degree is even, so the graph rises to the left and to the right.

B. Turning Points: N – 1 = number of turning points N represents the highest degree 6 – 1 = 5 turning points

We also need to know the end behavior of our roller coaster and the number of its turning points.

C. Zeroes

1 |-7 |7 |35 |-56 |-28 |48 | |2 | |1 |-5 |-3 |29 |2 |-24 | |1 | | |2 |-10 |-6 |28 |4 |-48 | | | | |1 |-4 |-7 |22 |24 | | | |1 |-5 |-3 |29 |2 |-24 |0 | | | |1 |-4 |-7 |22 |24 |0 | | | |

1 |-4 |-7 |22 |24 | |3 | | | |1 |-1 |-10 |-8 | |4 | | | |3 |-3 |-30 |-24 | | | | | | |4 |12 |8 | | | | |1 |-1 |-10 |-8 |0 | | | | | |1 |3 |2 | | | | | |

1 |3 |2 | |-1 | | | | | |1 |2 | |-2 | | |-1 |-2 | | | | | | | | |-2 | | | |1 |2 |0 | | | | | | | |1 |0 | | | |
Zeroes: 1, 2, 3, 4, -1, -2

D. X – Intercepts
(1, 0) (2, 0) (3, 0) (4, 0) (-1, 0) (-2, 0)

E.Y – Intercept (0, 48)
P(0) = (0)6 – 7(0)5 + 7(0)4 + 35(0)3 – 56(0)2 – 28(0) +48 = 48

Some of the few things we also need to know is the zeroes, X – Intecepts, and Y – Intercepts of our polynomial function.

Done! Now we only have to plot our points on the Cartesian Plane!. But before the fun happens, How did WE get our polynomial function in the first place? Now that’s easy, let me show you!

First we thought of the numbers we wanted to be the polynomial function’s factors ( the x – intercepts or should I say the ‘points’ we will put on the cartesian plane later ).
THEN WE MULTIPLY!!!

Result

The roller coaster’s highest point will be 153m above the ground. Even taller than the London Eye!

153m

20m 10m