**If there are edit (or mistakes) in the project wording, edits will appear in orange below:**

- No edits at this time.

**Instructions:**

- Print (or write on notebook paper) the task below.
- READ THE PROMPT AND QUESTIONS FULLY AND CAREFULLY!
- Fully and completely provide answers and solutions to each prompted question (the more informationyou provide, the more evidence I have to find complete solutions).
- You can only use this project to earn credit for F.IF.8, not any other standard.

**Standard:**

F.IF.8a – Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

• Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

**Success Criteria:**

- Students can factor, complete the square or use the quadratic formula to find zeros of quadratic functions.
- Explain the meanings of vertex and zeros in the context of a real-life application.
- Recognize patterns or symmetry in graphical or tabular representations.

**A Note on Cheating and Plagiarism:**

Purdue University’s Online Writing Laboratory (https://owl.english.purdue.edu/owl/) features Preventing Plagiarism as one of its resource areas. OWL lists the following common types of plagiarism

- Excessive repetition (poor paraphrasing of another’s words)
- Improper citation (failure to cite properly)
- Improper idea borrowing (failure to cite another’s ideas)
- Fraud (creation of false sources)
- Forgery (turning in another person’s work as your own)

Please consider the following guidance on identifying and avoiding Improper Citation, Improper Idea Borrowing, and Forgery.

**Improper Citation**

- Identifying characteristics: Missing, incomplete, or incorrect citation, either intentionally or unintentionally, of any source of text, media, etc. used in an assignment, assessment, report, project, or paper.
- Remedy: Follow the specified style sheet (e.g. APA or MLA) to both identify the source where it is placed in your document and give the full reference on your “Works Cited” or “References” page. If a style sheet is not specified, follow the rules of the one you know.
- Example: use the full URL of a Website.

**Improper Idea Borrowing**

- Identifying characteristics: Ideas, concepts, thoughts, or insights gained from media, conversations, demonstrations, lectures, friends, family, tutors, etc.
- Remedy: Follow the specified style sheet if one can be applied, otherwise state who, when, and what the other person contributed. For example, help received on a homework problem would be addressed with a statement like “Trillian helped me with question 2. b) by showing me how to complete the square so I could factor the polynomial.”

**Forgery**

- Identifying characteristics: Copying another person’s work, either by scan, photo copy, by hand, or any other method. Merely stating “I copied this from ____…” does not absolve the copier from the commission of plagiarism.
- Remedy: Do not copy!

This PDF guide is meant to serve as a starting point to understanding what completing the square means visually and how to accomplish it for a simple case. More advanced cases will not be assessed but will help overall understanding and understanding in future courses.

**A GUIDE TO COMPLETING THE SQUARE (PDF)**

For additional resources see these links:

- Full Guide to Completing the Square (Math Is Fun, with visuals)
- Completing the Square (purple math, more technical)
- Khan Academy Guide (several videos and exercises)

https://youtu.be/rS4vopTTp_8

- A.SSE.2 – Use structures of an expression to identify ways to rewrite it.
- A.SSE.3 – Factor to identify the roots or complete the square to solve for roots of a quadratic function.
- A.APR.6 – Divide Polynomials using the Tabular Method or Long Division.
- A.REI.4 – Solve quadratic equations in one variable.
- F.IF.7 – Graph functions expressed symbolically and identify key features

- A.SSE.1 – Interpret parts of an expression such as term, factor, and coefficient.
- A.SSE.2 – Use the structure of an expression to rewrite them into equivalent forms (factoring, dividing, multiplying polynomials).
- A.APR.1 – Add, Subtract & Multiply Polynomials
- A.APR.2 – Apply the Remainder Theorem (rewrite division problems as multiplication problems plus the remainder).

- Adding and Subtracting Polynomials
- Using Area to understand Distribution & Factoring
- Multiplying Polynomials Classwork
- Multiplying Polynomials HW
- Dividing Polynomials – Reverse Tabular (Lesson 3)
- Long Division w/ Polynomials (Lesson 4)
- Putting It All Together (Addition, Subtraction, Multiplication & Division) – Lesson 5
- Answers Guide Video (see description for specific question time stamps)
- Lesson 5 Teacher Guide

- Math Hospital (Polynomial Arithmetic)
- Explanation Video (see link for timestamps)

F.IF.6 – Average Rate of Change

A.CED.3 – Systems of equations and inequalities

A.REI.11 – Using function notation and determining the meaning of f(x) = g(x)

- https://www.khanacademy.org/math/algebra/algebra-functions/functions-average-rate-of-change/v/introduction-to-average-rate-of-change
- https://www.khanacademy.org/math/algebra/algebra-functions/functions-average-rate-of-change/v/average-rate-of-change-example-3
- https://www.khanacademy.org/math/algebra/algebra-functions/functions-average-rate-of-change/v/average-rate-of-change-when-function-defined-by-equation

- Step-by-Step Example (written)
- Graphing Inequalities (Video 1)
- Graphing Inequalities (Video 2)
- Graphing Inequalities (Video 3)
- Graphing Systems (Video 1)
- Graphing Systems (Video 2)

- https://www.khanacademy.org/math/algebra2/advanced-functions/systems-of-quadratic-equations/v/non-linear-systems-of-equations-1
- https://www.khanacademy.org/math/algebra2/advanced-functions/systems-of-quadratic-equations/v/systems-of-nonlinear-equations-3

- Average Rate of Change Practice Problems
- Linear Inequalities Homework (with answers)
- More Inequalities and Systems Problems (with answers)
- Function Notation and Systems of Equations by Graphing (with answers)
- PowerPoint Slides (with Notes)

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F.IF.1 – Students understand the basics of functions including input (domain) and output (range).

F.IF.2 – Use function notation and evaluate functions using the proper order of operations. See functions in different ways (e.g. tables, graphs, f(x), ordered pairs)

Review working with variables, how to work with variables when adding and multiplying.

- Syllabus & Consent Form
- Mathematical Habits of Mind
- Math Reflection Journal (to print)
- Additional Practice
- Order of Operations (PEMDAS)
- Function Notation & Evaluating Functions (engage in all 7 parts, see left column for focus areas).

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I look forward to an exciting year with you.

-Mr. Germanis

I look forward to an exciting year with you.

-Mr. Germanis

Meanwhile, take a look around and check out some of my favorite videos below!