# Ch 9: Big Ideas Math Algebra 1 - Chapter 9: Solving Quadratic Equations

### About This Chapter

## How It Works:

- Identify the lessons in the Big Ideas Math Solving Quadratic Equations chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the quadratic equations 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:

- The product and quotient rules
- How to find cube roots
- How to rationalize denominators
- How quadratic equations can be solved by graphing
- The process of completing the square
- Steps involved in finding maximum and minimum values
- How to solve quadratic equations with the quadratic formula
- What the discriminant is and how to find it
- How to solve systems of nonlinear equations in two variables
- How to estimate solutions of equations and nonlinear systems

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 1. Factoring Radical Expressions

Watch this video lesson to learn how to apply the product rule to your radical expressions. Learn how this product rule actually helps you to simplify your radicals as well.

### 2. Simplify Square Roots of Quotients

The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

### 3. How to Find the Cube Root of a Number

After watching this video lesson, you will understand the process of finding the cube root of a number. Learn which numbers have an easy cube root to find and what the cube root means.

### 4. Rationalizing Denominators in Radical Expressions

Radical expressions containing denominators are not simplified completely unless the denominator is free of radical symbols. This lesson will teach you how to remove a radical from the denominator of a fraction through a process called rationalizing the denominator.

### 5. Solving Quadratic Equations with Square Roots or Graphing the Function

Quadratic equations can be solved in many ways, including taking square roots and graphing the function. In this lesson, learn how to use these techniques to solve quadratic equations.

### 6. 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.

### 7. 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!

### 8. 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.

### 9. 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.

### 10. Discriminant: Definition & Explanation

The discriminant helps you to solve quadratic equations. In this lesson, you will learn how to identify the discriminant and how to use it to help you find the number of solutions in a quadratic equation.

### 11. Solving Systems of Nonlinear Equations in Two Variables

In this lesson, we will take a look at how to solve non-linear systems of equations in two variables by exploring two solving techniques for these types of systems - graphing and substitution.

### 12. Approximate Solutions of Nonlinear Systems & Equations

This lesson will explain how to approximate solutions of nonlinear systems of equations. We will explore different types of nonlinear graphs and methods for determining approximate solutions using these graphs.

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### Other Chapters

Other chapters within the Big Ideas Math Algebra 1: Online Textbook Help course

- Big Ideas Math Algebra 1 - Chapter 1: Solving Linear Equations
- Big Ideas Math Algebra 1 - Chapter 2: Solving Linear Inequalities
- Big Ideas Math Algebra 1 - Chapter 3: Graphing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 4: Writing Linear Functions
- Big Ideas Math Algebra 1 - Chapter 5: Solving Systems of Linear Equations
- Big Ideas Math Algebra 1 - Chapter 6: Exponential Functions & Sequences
- Big Ideas Math Algebra 1 - Chapter 7: Polynomial Equations & Factoring
- Big Ideas Math Algebra 1 - Chapter 8: Graphing Quadratic Functions
- Big Ideas Math Algebra 1 - Chapter 10: Radical Functions & Equations
- Big Ideas Math Algebra 1 - Chapter 11: Data Analysis & Displays