# Ch 20: Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics

### About This Chapter

## Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics - Chapter Summary and Learning Objectives

Our instructors strive to make the learning process efficient and enjoyable. In this chapter, you'll explore how to use FOIL, identify parabolas in real life and solve quadratic equations numerous ways. In each lesson, you'll find an engaging video to help illustrate the material. After each lesson, you can take a self-assessment quiz to test how well you've absorbed the information. If you need further assistance, reach out to the instructor for help. By the end of this chapter, you'll have learned about:

- Parabolas and their various forms
- Methods for solving quadratic equations
- Multiplying binomials using FOIL and the area method
- Factoring quadratic equations

Video | Objective |
---|---|

What is a Parabola? | Learn how identify and discuss parabolas. |

What is a Quadratic Equation? - Definition & Examples | Discover quadratic equations. |

Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero | Explore several methods for solving quadratics. |

Solving Quadratic Inequalities Using Two Binomials | Examine processes for solving quadratic inequalities. |

How to Use the Quadratic Formula to Solve a Quadratic Equation | Solve quadratic equations using the quadratic formula. |

How to Solve Quadratics That Are Not in Standard Form | Use the quadratic formula to solve quadratics that aren't in standard form. |

Parabolas in Standard, Intercept, and Vertex Form | Understand and determine value for three types of parabolas. |

Multiplying Binomials Using FOIL and the Area Method | Explore all the methods for multiplying binomials. |

Multiplying Binomials Using FOIL & the Area Method: Practice Problems | Practice multiplying binomials using various approaches. |

How to Factor Quadratic Equations: FOIL in Reverse | Examine the process for factoring quadratic equations. |

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient | Learn to factor quadratics with numbers other than 1. |

### 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. 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.

### 3. Solving Quadratics: Assigning the Greatest Common Factor and Multiplication Property of Zero

When it comes to solving quadratics, we have at our disposal several methods. Watch this video lesson to learn one such method you can use to solve quadratics that don't have a constant term.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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!

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### Other Chapters

Other chapters within the Honors Algebra 1 Textbook course

- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- Honors Algebra 1: Pre-Calculus Geometry
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math