About This Chapter
Factoring & Solving Quadratic Equations - Chapter Summary
As you go through these lessons on factoring and solving quadratic equations, you can get a better understanding of what's involved in completing the square and graphing circles and using the quadratic formula. Expert instructors also explain how the FOIL method is used in reverse. By the end of the chapter, you should be ready to:
- Solve polynomial problems that have a non-1 leading coefficient
- Discuss the use of factoring to solve a quadratic equation
- Recount how to solve quadratics that are not in standard form
- Identify the center and radius when graphing circles
- Describe what's involved in finding the equation of a circle
- Outline use of the FOIL method to multiply binomials
- Detail how to solve systems of equations involving circles, lines and parabolas
The engaging video lessons in this chapter can help to ensure you are fully adept at factoring and solving quadratic equations. A short quiz is available for each lesson to test your knowledge of the topics covered. You can even track your quiz results on your personal Dashboard. You can also print the lesson quizzes and use them as study worksheets.
1. Multiplying Binomials Using FOIL and the Area Method
From the distributive property, to FOIL, to the area model, to happy faces and claws, there are many different ways to learn how to multiply binomials. In this lesson, you'll learn how to use all of them and get to pick which one you like the most.
2. How to Factor Quadratic Equations: FOIL in Reverse
So, you know how to multiply binomials with the FOIL method, but can you do it backwards? That's exactly what factoring is, and it can be pretty tricky. Check out this lesson to learn a method that will allow you to factor quadratic trinomials with a leading coefficient of 1.
3. Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient
Once you get good at factoring quadratics with 1x squared in the front of the expression, it's time to try ones with numbers other than 1. It will be the same general idea, but there are a few extra steps to learn. Do that here!
4. 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.
5. Completing the Square Practice Problems
Completing the square is one of the most confusing things you'll be asked to do in an algebra class. Once you get the general idea, it's best to get in there and actually do a few practice problems to make sure you understand the process. Do that here!
6. 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!
7. How to Use the Quadratic Formula to Solve a Quadratic Equation
When solving a quadratic equation by factoring doesn't work, the quadratic formula is here to save the day. Learn what it is and how to use it in this lesson.
8. How to Solve Quadratics That Are Not in Standard Form
It isn't always the case that your equation will be set up nicely for you to solve. In this lesson, learn how to factor or use the quadratic formula to solve quadratic equations, even when they are not in standard form.
9. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
10. How to Find the Equation of a Circle
There are two commonly used forms of equations for a circle, in this lesson we'll take a few minutes to examine and understand both forms, and be able to convert from one to the other.
11. Solving Systems of Equations Involving Lines, Circles & Parabolas
This lesson provides instruction for how to solve systems of equations involving lines, circles and parabolas by graphing each on the coordinate plane and finding the points of intersection.
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 CLEP Precalculus: Study Guide & Test Prep course
- Recognizing Functions
- Working with Exponential and Logarithmic Functions
- Piecewise and Composite Functions
- Functions as Models
- Understanding, Solving & Graphing Inequalities
- Understanding Linear Equations
- Radical, Rational and Absolute Value Equations
- Parabolas, Ellipses and Hyperbolas
- Exponents and Polynomials
- Geometry and Trigonometry
- Using Scientific Calculators
- CLEP Precalculus Flashcards
- Additional CLEP Precalculus Flashcards