Virtual High School Mathematical Calculations Questions

Your task in this assignment is to use polynomial functions to design a rollercoaster. To express your rollercoaster design you will create a piecewise function out of the polynomial functions. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.

Your rollercoaster must meet certain criteria, and the questions below will guide you through this process. In the end, you will submit a written assignment, showing all of your calculations and ideas, to the dropbox. You may find it very useful to utilize graphing technology, such as Graph, to help you with this assignment.

QUESTION 1

Research a favourite, or a famous, rollercoaster. Write a short summary (2-3 paragraphs) of this coaster’s general information; include its name, a picture, where it is located, when it was built, why you picked it and its physical characteristics.

Make sure you note the height of the initial drop as the initial drop of the rollercoaster you will be designing in this assignment will model the initial drop of this rollercoaster you have researched. Also remember to cite your sources (1-2 sources).

QUESTION 2

It may be useful now to do a little bit of research on the physics of rollercoasters. You will not need to do any physics-style calculations in this assignment, but you will be expected to abide by the common rules. For example; a rollercoaster cannot be expected to defy gravity, it must be given momentum at the beginning of the track, and cannot reach as high a height at the end of its track as it can at the beginning.

Write a short paragraph describing what you found and cite your sources (1-2 sources) .

QUESTION 3

Now it is time to create your own rollercoaster. Using the idea of piecewise functions, create an appropriate scale on your axes and design a rollercoaster, using technology like Graph. You rollercoaster must have the features listed below. If you are unsure about piecewise functions, or how to express them, this is a good time to do some independent research on their proper use and notation.

You should try to make each of the polynomial functions flow into one another to create a smooth ride for your passengers. To prevent your functions from overlapping, make sure to restrict the domain of the function. Set each polynomial function to a different colour and submit a picture (or a screen capture) of your design, as well as the piecewise function notation that models it.

.

Models the initial drop of the rollercoaster you researched

Has at least 4 other drops.

Goes through an underground tunnel at least once (assuming y = 0 is the ground)e) Any other features you feel would add to the ride and can be modelled with a polynomial function.QUESTION 4For each of the pieces in your design:

d)

QUESTION 5

Suppose you were asked to take the first three pieces of your rollercoaster and model them with a single function. Answer the following questions:

b)

Determine an equation for this function.

c)

Engineering a Rollercoaster Mid-Unit
Assignment
You may choose to complete your mathematical calculations by hand and scan them or take
images to upload to the dropbox. To help your teacher review your work, submit your calculations
as a single file document (preferably as a pdf). If you aren’t sure how to do this, email your teacher
for assistance.
Important
When answering questions in a mathematics course always use the following auidelines to
help you do your best:
inis assignment contains a questions.
. This assignment has no time limit.
• Provide full solutions, showing all of your steps.
• Include only one step or idea per line.
• Use one equal sign per line.
• Line up equal signs vertically.
• Don’t use self-developed short form notations.
Polynomial functions are versatile. They can be manipulated to just about any shape and size and
can model a wide variety of real-life events and objects. In this assignment, you will be taking on the
role of an engineer and presenting a design for a rollercoaster using polynomial functions.
The instructions within the assignment will outline the process in detail.
Rubric
Please navigate to the next page to see the rubric for this assignment and use it to ensure you are
meeting all of the expectations of this assignment.
Once completed, your assignment should be submitted to the corresponding Dropbox: “Engineering
a Rollercoaster Mid-Unit Assignment”.
Also note, if you are citing any resources, use APA citation style. Research APA, or use this
resource as a guide:
Purdue OWL: APA Format