About This Chapter
Below is a sample breakdown of the Polynomial Functions Basics chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Understanding polynomial functions||Polynomials, coefficient, leading coefficient, degree, term, leading term, evaluating polynomials in function notations|
|Tuesday||Graphing basic polynomials||First degree polynomials on a graph, sign-on intervals, the large-scale behavior of a function|
|Wednesday||Intervals, behaviors, graphing higher degree polynomials||Determining polynomial functions' intervals; polynomials' short run and long run behavior; cubics, quartics and quintics on a graph|
|Thursday||Pascal's Triangle||Pascal's Triangle, using coefficients|
|Friday||Binomial theorem||Definition and usage of 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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