Module 3 Project

This project will be completed in four parts throughout the module. Be sure to keep all of your work from the project in your course folder, as you will need to hand it in for assessment at the completion of Lesson 9. When you have fully answered all questions from all four parts and have completed the data tables and graphs as instructed, submit your work, including your rubric, to your teacher.

 

The Module 3 Project involves using quadratic functions to compare the trajectories produced by three different teams in an egg-launch contest. You will use the skills learned in Module 3 to compare the heights and distances of the tossed eggs using tables, graphs, and equations. You will have to convert between these methods of expression to decide the winner of the egg-launch contest.

 

Background

 

Three pitchers on the Shaunavon High School softball team were bragging about how far they could throw a ball. Their coach decided to let them show off their skills. Coach Laflame came up with the following challenge after talking to the pitchers’ math teacher.

 

Each pitcher was given one egg and was to throw the egg as far from home plate as possible. Each pitcher chose a team from the math class to help with the challenge. Each team was assigned mathematical tasks related to the paths of the tossed eggs. The three teams were Team Alfredo, Team Min, and Team Zawati—each named after the pitchers.

 

Team Zawati

 

Team Zawati determined that their egg followed the path given by the function f(x) = −0.0075x2 + 1.45x + 2, where x is the distance from home plate and f(x) is the height of the egg. Both distance and height were measurerd in feet.

 

Team Min

 

Team Min used time-lapse photography to capture the flight of their egg. The team used the images to create the following graph of the path of the egg.

 

 

Team Alfredo

 

Team Alfredo used some high-tech equipment from the physics lab and recorded the following data.

 

Distance from Home Plate (feet)	Height Above Ground (feet)
0	2
7	5.84
28	15.44
56	23.76
77	26.64
88	27.49
112	25.04
126	22.16
147	15.44
168	5.84
176	2

 

Which team do you think won the challenge?

 

Part 1: Preparing the Data for Team Zawati

 

You will complete Part 1 as part of your assessment for Lesson 3. Answer the following questions. Make sure to save all of your work to your course folder.

 

Provide complete solutions to each question. If a graphing solution is used, provide appropriate window settings. If an algebraic solution is needed, show all necessary steps.

 

Team Zawati provided a function for the path of their egg. Complete the following tasks using the function f(x) = −0.0075x2 + 1.45x + 2.

1. Complete Part 1 Chart to develop a table of values showing points on the egg’s path. Choose appropriate values for the distance in feet, and then mathematically find the height above the ground. Show all work for at least two points.
   
   
2. Sketch a graph of the path of the egg. You can use 1-cm Grid Paper to sketch your graph, or you can create your graph electronically.
   
   
3. Find the highest point on the egg’s path. Using the table of values you created is not enough.
   
   
4. Find the distance the egg travelled horizontally. Using the table of values is not enough.

Remember to save your work from Part 1 in your course folder. Return to Lesson 3.

 

Part 2: Preparing the Data for Team Min

 

You will complete Part 2 as part of your assessment for Lesson 5. Answer the following questions. Make sure to save all of your work to your course folder.

 

Provide complete solutions to each question. If a graphing solution is used, provide appropriate window settings. If an algebraic solution is needed, show all necessary steps.

 

Team Min provided a graph showing the path of its egg. You can obtain information from Team Min’s data by opening the applet titled Team Min and moving the blue dot, labelled B, on the graph.

 

1. Using the applet, go to Part 2 Chart to develop a table of values showing points on the egg’s path.
   
   
2. Find a function that describes the path of the egg. Show the method you used to find the equation.
   
   
3. State the highest point on the egg’s path.
   
   
4. Find the distance the egg travelled horizontally.

Remember to save your work from Part 2 in your course folder. Return to Lesson 5.

 

Part 3: Preparing the Data for Team Alfredo

 

You will complete Part 3 as part of your assessment for Lesson 7. Answer the following questions. Make sure to save all of your work to your course folder.

 

Provide complete solutions to each question. If a graphing solution is used, provide appropriate window settings. If an algebraic solution is needed, show all necessary steps.

 

Team Alfredo provided a table of data about the path of its egg.

1. Find a function that describes the path of the egg. Show the method you used to find the equation.
   
   
2. Sketch a graph of the path of the egg. You can use 1-cm Grid Paper to sketch your graph, or you can create your graph electronically.
   
   
3. Confirm the highest point on the egg’s path graphically. Provide a screenshot. Does this match your original table of values? Why or why not?
   
   
4. Create a graph to confirm the distance the egg travelled horizontally. Provide a screenshot. Does this match your original table of values? Why or why not?
   
   
5. Write the quadratic function in standard form.
   
   
6. Confirm algebraically the distance the egg travelled horizontally.

Remember to save your work from Part 3 in your course folder. Return to Lesson 7.

 

Part 4: Comparing and Working with the Data

 

You will complete Part 4 as part of your assessment for Lesson 9. Answer the following questions. Make sure to save all of your work to your course folder.

1. Which pitcher’s egg travelled the farthest from home plate?
   
   
2. Which pitcher’s egg rose the highest?
   
   
3. Create a challenge so that the pitcher that did not win either the distance-travelled challenge or the height-reached challenge will win.

Assessment

 

Review the Module 3 Project Rubric to ensure you understand how you will be assessed. Use the rubric to evaluate your project and reflect on the process you used. Make any changes you feel would make your work better. Submit your completed rubric with your project.

 

Submit the work from the Module 3 Project to your teacher at this time. Then return to Lesson 9.