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Parametric Equations

Student Guide

Student Guide (continued)

Assignment Summary

For this assignment, you will represent hiking itineraries with parametric equations and use those equations to make predictions.

Background Information

Parametric equations are a set of functions defined in terms of a parameter. A parametric equation contains a horizontal and a vertical component that are both defined in terms of the parameter. The parameter can be eliminated to create a rectangular equation.

Assignment Instructions

For this project, you are expected to submit the assignment.

Step 1: Prepare for the performance task.

a) Read through the guide before you begin so you know the expectations for this assignment.

b) If there is anything that is not clear to you, be sure to ask your teacher.

c) If your word-processing program has an equation editor, you can insert your equations here. Otherwise, print this activity sheet and write your answers by hand.

Step 2: Complete Parts 1 and 2 in the Assignment section of this document.

a) Read all directions carefully.

b) Complete each task.

c) Insert images or screenshots of graphs when needed. Be sure that all graphs or screenshots include appropriate information such as titles, labeled axes, etc.

d) Be sure to show all your work. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.

e) Consider underlining and circling important components in the problems.

Step 3: Evaluate your project using this checklist.

If you can check each box below, you are ready to submit your project.

· Have you answered all questions in Part 1 and Part 2?

· Have you shown your work?

· Did you include an image or screenshot of a graph when requested?

· Are all your equations correct? Be sure to check your formatting carefully.

Step 4: Revise and submit your project.

a) If you were unable to check off all of the requirements on the checklist, go back and make sure that your project is complete. Save your project before submitting it.

b) Your teacher will give you further directions about how to submit your work. You may be asked to submit your responses through the virtual classroom, email it to your teacher, or print it and hand in a hard copy.

c) Congratulations! You have completed your project.


Part 1: Write parametric equations to represent a mountain hiking trail.

The table shows the estimated distances and elevation changes between a base camp and various locations along a popular mountain trail. The distance traveled along the trail is represented by x, the elevation is represented by y, and the time from the base camp to each location is represented by t.


Distance from Base Camp


Travel Time from Base Camp

Base Camp

0 miles

6,990 feet

0 hours

Camp I

4 miles

8,290 feet

10 hours

Camp II

8.4 miles

10,875 feet

21 hours

Camp III

11.4 miles

13,331 feet

28.5 hours

Camp IV

14.8 miles

16,795 feet

37 hours


17.2 miles

19,675 feet

43 hours

1. Use the data points about the distance and elevations of the camps to graph the data points where the x-coordinate is the total distance traveled from the base camp and the y-coordinate is the elevation. Use the grid below or include a screenshot of the data plotted from a calculator. (5 points)

2. Describe the curve in the graph by completing the steps.

a) Find a reasonable interval for the values of and explain its significance. (10 points)

b) Write a linear function, x(t), for the total distance in miles hiked in terms of total time hiking in hours using the data from the table. (5 points)

c) Write a quadratic function, y(t), for elevation in terms of the total time hiking in hours using the data in the table. Find a system of three equations and three unknowns to write the equation. (10 points)

Part 2: Write and use the rectangular form of the parametric equations.

1. Using the equations from Part 1, eliminate the parameter, and write the rectangular form of the equation. (10 points)

2. Use the rectangular equation to show the elevation that a group can expect to reach after hiking 8 miles. Then determine the time it will take the group to get to that point on the mountain. (6 points)

3. Use the rectangular equation to show approximately how far a group can expect to hike before reaching an elevation of 12,000 feet. (4 points)

Copyright © Edgenuity Inc.

Copyright © Edgenuity Inc.

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