**Algebra 2**

**Fall Project 2014**

__Purpose__The purpose of this project is for you to develop your own quadratic equation based on a real-world application. Although we study quadratic equations in an abstract sense in the classroom, quadratic equations, and their graphs, appear in many real-life situations from falling objects, launching objects, and even in economics. For this project, you will be tasked with launching an egg into the air and modeling its trajectory with the use of a quadratic equation. You may use any resources available to you including your text book and internet.

__Requirements__You and your group will be required to launch an egg into the air and investigate its trajectory with the use of quadratic equations. You will need to design, or buy, a launching apparatus, and then determine how to find the quadratic equation that models your egg’s flight through the air.

You will also answer questions based on the data you collect and the equation that you develop. Creativity will be needed in order to determine how to develop your quadratic equation. You and your group will also need to write a 2-page paper explaining the processes you used, how you came up with your quadratic equation, and any errors that may have resulted from your experimentations. This paper will be graded for correct grammar, punctuation, etc. The paper must be written in Times New Roman style with 12 point font. You also describe how you developed your quadratic equation and show the mathematics involved in that development. Your paper must also include a neat, detailed graph of your quadratic equation. This paper will serve as the means for you to explain the analysis you used and the procedures you followed to develop your quadratic equation during this project. (Much like a diary would do.) This is a collaborative effort amongst the group and only one paper needs to be submitted from each group.

__Grading__Although this project is a group project, it is possible for each group member to receive different grades based on the amount of participation provided by each member. At the end of this project, each group member will fill out a rubric to grade their team member(s) on participation. This, along with my grade, will be factored into the overall final grade. This project will be worth 150 points, and failure to complete the project will result in an F for the quarter grade, regardless of your overall percentage. Each step of the project will have a due date to help you remain on task. (See the last page of this project for due dates and deadlines.) I have included the rubrics that will be used in grading these projects so that you can see exactly what I will be looking for in your papers.

Extra credit will be given to groups who go above and beyond the requirements of this project. For example, if you create a poster board of your project, detailing each step of your journey through this project with diagrams and equations, then you will be rewarded with extra credit. These projects that demonstrate a high level of creativity, accuracy, neatness, and knowledge will be displayed in the math hallway.

**Project Due Dates and Deadlines**

Partners chosen Friday, October 10

Apparatus designed or purchased Friday, October 24

First testing day (outside) Monday, October 27

Final testing day (All data collected) Friday, November 7

Rough draft of paper and graph due Friday, November 14

Final paper and project due Tuesday, November 25

**Breakdown of points:**

2 Page Paper 50 Points

Mathematics/Problem Solving 90 Points

Collaboration/Working Skills 10 Points

**Questions to answer and address in your paper:**

**1.**What equation most effectively models the path of your egg in flight? Write the equation.

**2.**Explain how your group developed this equation. What techniques did you use?

**3.**What is the maximum height your egg will reach based on your equation?

**4.**What is the maximum distance your egg will travel based on your equation?

**5.**What do the zeros of your equation represent in terms of this project?

**6.**Write your equation as a function in terms of distance, x, and height, y.

**7.**What would f(5) and f(10) equal? What does this represent in terms of your egg’s path?