About This Chapter
Who's it for?
This unit of our High School Trigonometry Homeschool Curriculum course will benefit any student who is trying to learn about polynomial functions basics. There is no faster or easier way to learn about polynomial functions. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about polynomial behavior, functions and graphs.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Polynomials Functions Basics unit exam confirm understanding or identify any topics that require review.
Polynomial Functions Basics Unit Objectives:
- Understand the terms used to describe polynomial functions.
- Learn how to use function notation to evaluate polynomials.
- Interpret and construct polynomial graphs.
- Understand the long-run and short-run behaviors of polynomial functions.
- Define and explain Pascal's Triangle.
- Define and explain the Binomial Theorem.
1. Terminology of Polynomial Functions
After watching this video lesson, you will be able to understand and use the words associated with polynomial functions like a pro. You will see words, such as leading coefficient, and you will immediately know what it is referring to.
2. How to Evaluate a Polynomial in Function Notation
This lesson will review how to evaluate polynomials in function notation. Along with an analogy to explain the process, examples will be given and worked during the lesson.
3. Understanding Basic Polynomial Graphs
This lesson will cover understanding basic polynomial graphs. The lesson focuses on how exponents and leading coefficients alter the behavior of the graphs.
4. Finding Intervals of Polynomial Functions
Watch this video lesson to learn how you can find the intervals of a polynomial function. Also learn how to find out whether each interval is negative or positive.
5. Short Run & Long Run Behavior of Polynomials: Definition & Examples
Watch this video lesson to learn how you can use the graph of a polynomial to help you explain the polynomial function. Learn how to explain the behavior of the polynomial at the origin and at the far ends.
6. How to Graph Cubics, Quartics, Quintics and Beyond
Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!
7. Pascal's Triangle: Definition and Use with Polynomials
Pascal's Triangle is defined and discussed briefly. Following the introduction to the triangle, its use in expanding polynomial powers is elaborated with examples.
8. The Binomial Theorem: Defining Expressions
In this lesson, students will learn the binomial theorem and get practice using the theorem to expand binomial expressions. The theorem is broken down into its parts and then reconstructed.
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Other chapters within the High School Trigonometry: Homeschool Curriculum course
- Types of Real Numbers: Homeschool Curriculum
- Working with Linear Equations: Homeschool Curriculum
- Graphing Inequalities: Homeschool Curriculum
- Absolute Value Equations: Homeschool Curriculum
- Complex Numbers: Homeschool Curriculum
- Using Systems of Linear Equations: Homeschool Curriculum
- Mathematical Modeling: Homeschool Curriculum
- Introduction to Quadratics: Homeschool Curriculum
- Quadratic Functions: Homeschool Curriculum
- Coordinate Geometry: Homeschool Curriculum
- Functions for Trigonometry: Homeschool Curriculum
- Function Operations: Homeschool Curriculum
- Graph Symmetry: Homeschool Curriculum
- Graphing with Functions: Homeschool Curriculum
- Higher-Degree Polynomial Functions: Homeschool Curriculum
- Difference Quotients: Homeschool Curriculum
- Function Graphs: Homeschool Curriculum
- Exponential Functions: Homeschool Curriculum
- Trigonometric Functions: Homeschool Curriculum
- Triangle Trigonometry: Homeschool Curriculum
- Trigonometric Graphs: Homeschool Curriculum
- Solving Trigonometric Equations: Homeschool Curriculum
- Trigonometric Identities: Homeschool Curriculum
- Trigonometric Applications: Homeschool Curriculum
- Analytic Geometry: Homeschool Curriculum
- Vectors, Matrices & Determinants: Homeschool Curriculum
- Polar Coordinates: Homeschool Curriculum
- Circular Arcs, Circles & Angles: Homeschool Curriculum