About This Chapter
Graphing and Factoring Quadratic Equations - Chapter Summary and Learning Objectives
Do you need to learn more about parabolas? Our video lessons will introduce you to, explain the components of and teach you the forms of parabolas. You'll learn vocabulary terms that include vertex, maximum, intercept, roots and axis of symmetry.
Have you used FOIL before? You probably have, but have you used it to work with quadratic equations? We have lessons that will help you learn to multiply from intercept to standard form using FOIL and to use FOIL when factoring quadratic equations. We also provide you with practice problems, so you can put your newly learned skills to use.
Are you ready to solve some quadratic equations? You'll want to watch our lessons that cover solving equations by factoring, solving quadratics that aren't in standard form and using two binomials when solving quadratic inequalities. Some of the concepts covered in these lessons include the zero product property and discriminants.
Do you know how to complete the square? If not, we have lessons that will teach you just how to do it. Again, we will provide you with some practice problems to try out your skills and allow you to ensure that you really understand how to do it.
Each of our engaging video lessons is designed to make learning quadratic equations accessible, straightforward, and even fun! All videos are taught by experts on the subjects, and assembled by professional video editors. Thanks for watching!
1. What is a Parabola?
A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.
2. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
3. 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.
4. Multiplying Binomials Using FOIL & the Area Method: Practice Problems
There are a few mistakes that are easy to make when multiplying binomials with FOIL and also a few ways to complicate problems like this, so why not make sure you're brushed up on your skills? You'll also learn a shortcut and how to use the area method to multiply even bigger polynomials.
5. 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.
6. 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!
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. 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!
9. 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!
10. 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.
11. 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.
12. Solving Quadratic Inequalities Using Two Binomials
Watch this video lesson to learn what simple steps you can take to solve quadratic inequalities using two binomials. See how it only requires a few steps to solve quadratic inequalities using this method.
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Other chapters within the Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102