About This Chapter
Quadratic & Polynomial Equations - Chapter Summary
If you're seeking to learn or gain additional information about quadratic and polynomial equations, this chapter can help! Top instructors have developed entertaining lessons you can use to discover or refresh your knowledge of the mathematical operations associated with quadratic equations, polynomial expressions and much more. By taking time to review this chapter, you will have the ability to:
- Understand the meaning of polynomials, binomials, quadratics and basic polynomial graphs
- Factor polynomial expressions
- Write polynomial equations by using rational and complex zeros
- Solve a quadratic equation by factoring
- Define and understand the equation for the quadratic formula
- Complete the square, then write the standard form of an equation
- Choose the correct method for solving quadratic equations
- Solve quadratic equations in a real-world context
Feel confident that you have a good grasp of quadratic and polynomial equations by tailoring this chapter's lessons to your schedule and study habits. Access the lessons anytime from any computer, smartphone or tablet. Review them in any sequence and revisit them as often as needed. When ready, assess your knowledge by taking short lesson quizzes and a chapter exam. If you need additional details about lesson topics, be sure to submit your questions to our experts.
1. What are Polynomials, Binomials, and Quadratics?
What do polynomials, binomials, and quadratics have in common? What are their differences? How can you identify each of them? Watch this video lesson to find the answers.
2. Factoring Polynomial Expressions
When it comes to factoring polynomials, there are several methods to choose from depending on what kind of polynomial you are looking at. Watch this video lesson to learn how to identify and use the appropriate method.
3. 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.
4. 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.
5. How to Solve a Quadratic Equation by Factoring
If your favorite video game, 'Furious Fowls,' gave you the quadratic equation for each shot you made, would you be able to solve the equation to make sure every one hit its target? If not, you will after watching this video!
6. What is the Quadratic Formula? - Definition, Equation & Proof
The quadratic formula is a method that is used to find the roots of a quadratic equation. In this lesson, you will learn about the history of the quadratic formula, how to use it, and prove it. A quiz at the end will solidify what you've learned.
7. How to Complete the Square
Completing the square can help you learn where the maximum or minimum of a parabola is. If you're running a business and trying to make some money, it might be a good idea to know how to do this! Find out what I'm talking about here.
8. Write the Standard Form of an Equation by Completing the Square
In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.
9. Deciding on a Method to Solve Quadratic Equations
There are several ways to solve quadratic equations, so how do you pick a good approach? In this lesson, we'll discuss a systematic method that helps you pick the best way to solve any quadratic equation that might cross your path.
10. Real World Interpretations of Quadratic Equations
You have probably heard the saying, 'What goes up must come down?' But did you ever wonder why? The physical force that causes this behavior is gravity. And the mathematical relationship that describes it is a quadratic equation.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the NY Regents Exam - Algebra I: Test Prep & Practice course
- Algebraic Units & Modeling
- Structure of Mathematical Expressions
- Polynomial Operations Basics
- Creating Equations, Inequalities & Expressions
- Solving & Graphing Equations & Inequalities
- Understanding Data Using Statistics
- Interpreting Linear Models
- Understanding Functions
- Interpreting, Analyzing & Graphing Functions
- Building Linear & Exponential Functions
- Basics of Rational & Irrational Numbers
- About the NY Regents Examinations
- NY Regents Exam - Algebra I Flashcards