About This Chapter
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.
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. 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.
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.
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.
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.
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.
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.
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.
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Other chapters within the Alberta Education Diploma - Mathematics 30-2: Exam Prep & Study Guide course
- Problem Solving with Logic & Reasoning
- Number Systems & Factoring
- Set Theory & Venn Diagrams
- Probability & Uncertainty
- Permutations & Combinations in Probability
- Introduction to Relations & Functions
- Rational Expressions & Quadratic Equations
- Logarithmic & Exponential Operations
- Sinusoidal Functions
- Alberta Education Diploma - Mathematics 30-2 Flashcards