About This Chapter
How it works:
- Identify the lessons in the Prentice Hall Algebra 2 Quadratic Equations and Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the quadratic equations and functions topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Parabolas in standard, intercept and vertex form
- Use of quadratic models to find minimum and maximum values
- Basic transformations of polynomial graphs
- How to solve a quadratic equation by factoring
- Solutions for quadratic trinomials by factoring
- Imaginary numbers
- How to complete the square
Prentice Hall Algebra 2 is a registered trademark of Pearson Education, Inc., which is not affiliated with Study.com.
1. What is a Quadratic Equation? - Definition & Examples
You might be surprised to learn that quadratic equations are an important part of the world we live in. We sometimes even make use of them for our entertainment! Watch this video lesson to learn more about these equations.
2. 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.
3. 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.
4. Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example
Minimum and maximum values are found in parabolas that open up or down. In this lesson, learn how to find the minimum and maximum values algebraically and graphically.
5. Basic Transformations of Polynomial Graphs
The basic transformations for a graph are movement up and down, left and right, pinched or stretched graphs, and flipped graphs. This lesson will review how to accomplish each of these transformations.
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 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.
8. 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!
9. Solving Quadratic Trinomials by Factoring
Factoring is a quick and easy way to find the solutions to a quadratic trinomial. Watch this video lesson to learn how you can use this method to solve your quadratics.
10. What is an Imaginary Number?
The imaginary number 'i' is the square root of -1. Although this number doesn't actually exist, pretending that it does allows us to do a bunch of crazy math that scientists use every day. Learn the basics of that number 'i' here!
11. How to Add, Subtract and Multiply Complex Numbers
Knowing that complex numbers exist is the first step. But that knowledge alone won't help you do much with them. Learn the basics of complex number addition, subtraction and multiplication here!
12. How to Solve Quadratics with Complex Numbers as the Solution
When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!
13. 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.
14. 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!
15. 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.
16. 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.
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Other chapters within the Prentice Hall Algebra 2: Online Textbook Help course
- Prentice Hall Algebra 2 Chapter 1: Tools of Algebra
- Prentice Hall Algebra 2 Chapter 2: Functions, Equations, and Graphs
- Prentice Hall Algebra 2 Chapter 3: Linear Systems
- Prentice Hall Algebra 2 Chapter 4: Matrices
- Prentice Hall Algebra 2 Chapter 6: Polynomials and Polynomial Functions
- Prentice Hall Algebra 2 Chapter 7: Radical Functions and Rational Exponents
- Prentice Hall Algebra 2 Chapter 8: Exponential and Logarithmic Functions
- Prentice Hall Algebra 2 Chapter 9: Rational Functions
- Prentice Hall Algebra 2 Chapter 10: Quadratic Relations and Conic Sections
- Prentice Hall Algebra 2 Chapter 11: Sequences and Series
- Prentice Hall Algebra 2 Chapter 12: Probability and Statistics
- Prentice Hall Algebra 2 Chapter 13: Periodic Functions and Trigonometry
- Prentice Hall Algebra 2 Chapter 14: Trigonometric Identities and Equations