Ch 9: Solving Problems with Polynomial Functions

About This Chapter

These lessons on solving problems with polynomial functions will teach you about basic polynomial graphs and cubic functions. The lessons in this chapter are valuable when preparing for a test or working on class assignments.

Solving Problems with Polynomial Functions - Chapter Summary

In these lessons on solving problems with polynomial functions, you will learn how exponents alter the behavior of graphs. You will also gain a clearer understanding of how to find x-intercepts and y-intercepts. By the end of the chapter, you should be positioned to:

  • Use terminology associated with polynomial functions
  • Explain basic polynomial graphs
  • Compare properties of functions graphically
  • Identify maximum and minimum values of a graph
  • Find and apply intercepts of a line
  • Use the rational zeros theorem and synthetic division to find rational zeros
  • Write polynomial equations using rational and complex zeros
  • Define cubic function

These lessons can help you quickly understand how to solve problems with polynomial functions. You have the option of reviewing all the lessons in the chapter, or just specific lessons based on your needs. A brief quiz is available for each lesson to test your knowledge.

8 Lessons in Chapter 9: Solving Problems with Polynomial Functions
Test your knowledge with a 30-question chapter practice test
Terminology of Polynomial Functions

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.

Understanding Basic Polynomial Graphs

2. 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.

Compare Properties of Functions Graphically

3. Compare Properties of Functions Graphically

In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.

How to Determine Maximum and Minimum Values of a Graph

4. How to Determine Maximum and Minimum Values of a Graph

What is the highest point on a roller coaster? Most roller coasters have a lot of peaks, but only one is really the highest. In this lesson, learn the difference between the little bumps and the mother of all peaks on your favorite ride.

How to Find and Apply the Intercepts of a Line

5. How to Find and Apply the Intercepts of a Line

How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.

Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

6. Finding Rational Zeros Using the Rational Zeros Theorem & Synthetic Division

After completing this lesson, you will know what the rational zeros theorem says. You will also know how to apply this theorem to find zeros of polynomial functions.

Using Rational & Complex Zeros to Write Polynomial Equations

7. Using Rational & Complex Zeros to Write Polynomial Equations

In this lesson, you will learn how to write a polynomial function from its given zeros. You will learn how to follow a process that converts zeros into factors and then factors into polynomial functions.

Cubic Function: Definition, Formula & Examples

8. Cubic Function: Definition, Formula & Examples

In this lesson, we will explore a specific function called a cubic function in mathematics. We'll define this type of function and look at some various examples involving cubic functions to help us to understand what cubic functions look like and how they can be used.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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