- F.LE.4 – For exponential models, understand the relationship between the exponent expression and the logarithmic expression. Evaluate where base is 2, 10 or e using technology.
- Evaluate logarithmic functions

- F.IF.7e – Graph logarithmic functions by hand, exploring the relationship with exponential functions (through tables and inverses). Identify key features and end behaviors.

- WhatPower (ENY Lesson 8) –> Relating to Exponential Functions
- WhatPower (ENY Lesson 10) –> Connecting to Logarithms (What is a Log?)
- Introduction to Logarithmic Properties (ENY Lesson 11)
- More Logarithmic Properties & Practice (ENY Lesson 12)

This unit will be focusing on exponential functions. We will start by reviewing exponent rules, looking at rational exponents (exponents that have fraction exponents), then we will use function notation to make data tables and graph those. There are MANY applications to exponents, many used in everyday life. We will explore how to create exponential expressions based on contexts to answer real world questions.

Standard | CCSS Language | Interpretation |

N.RN.1 | Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example 51/3 is the cube roots of 5 because we want (51/3)3 = (53)1/3 | Convert rational exponents into roots & use exponent rules to simplify. |

A.SSE.1b | Interpret complicated expressions by viewing one or more of their parts as a single entity. (i.e. I = P(1+r)^t student can identify the principal, rate and time interval) | Within a context, interpret the parts of an exponential function. (i.e. I = P(1+r)^t student can identify the principal, rate and time interval). |

A.CED.1 | Create equations and inequalities in one variable and use them to solve problems. Including exponential functions. | Students can create an equation modeling a simple situation using exponents. Answers simple questions using their designed model. |

F.IF.7e | Graph exponential and logarithmic functions showing intercepts and end behavior. | Graph exponential functions by creating a table or identifying key parts. Can distinguish between growth and decay. |

Day 1: Exponent Laws Discovery Activity

Day 2: Drug Filtering Worksheet

Day 3/4: Bees Gone Crazy Task – Exponential Functions

Day 4: Who is right, who is wrong (answers)

]]>There are four major types of transformations we study in Algebra 2. For us, these types of functions are helpful for using when modeling the real world around us, like throwing a football or measuring how quickly the tires on our car is rotating so we don’t get a speeding ticket. The video below will help you transform parent functions to meet specific criteria.

Using our understanding about finding zeros of polynomials and patterns that exist for higher order polynomials, we can make rough sketches of polynomials based on their factored equations. This video will help explain the logic behind graphing higher order polynomials.

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The videos above may be helpful, but you might be looking for class activities.

- Day 1 Special Types of Ones
- Day 1 Extra Practice
- Day 2 Multiplying and Dividing Rational Expressions
- Day 2 Multiplying and Dividing Rational Expressions (extra Practice

**There are several pieces of information that need to come together to find success at simplifying rational expressions. Here are the basics:**

- Simplifying Rational Expressions – Stating Exclusions
- Multiplying/Dividing Rational Expressions – Stating Exclusions
- Adding and Subtracting Rational Expressions – Stating Exclusions

- Factoring Quadratics 1
- Factoring Quadratics 2
- Factoring Quadratics 3
- Factoring by Grouping 1
- Factoring by Grouping 2
- Factoring by Grouping 3

**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)

- 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)