# Ch 15: High School Algebra: Graphing and Factoring Quadratic Equations

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### About This Chapter

## Graphing and Factoring Quadratic Equations - Chapter Summary and Learning Objectives

This chapter is tasked with showing how real-world algebraic data can be displayed through graphs and tables. In these lessons our instructors will teach you how factor and solve quadratic equations. You will also come to know the difference between trinomials, polynomials and binomials. We offer a few lessons that allow you to practice concepts through examples that we supply. This chapter is designed to teach you how to:

- Identify and define the different parts of a parabola
- Use the FOIL technique to multiply binomials
- Factor to solve a quadratic equation
- Plot points on a scatter plot and line graphs
- Complete the square

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

Tables and Graphs in the Real World | Explain how tables and graphs are just another way to display information relating to algebra. |

Scatterplots and Line Graphs | Define and discuss how to use scatterplots and line graphs. |

What is a Parabola? | Learn where we see parabolas in real life; vertex, maximum, intercepts/roots; and axis of symmetry. |

Parabolas in Standard, Intercept and Vertex Form | Learn the 3 forms of parabolas and interpret the a value in each form - standard, vertex and intercept form. |

Multiplying Binomials Using FOIL and the Area Method | Learn how to use the FOIL method. |

Multiplying Binomials Using FOIL and the Area Method: Practice Problems | Get practice FOILing and using the area method. |

How to Factor Quadratic Equations: FOIL in Reverse | Learn how to factor. |

Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient | Get practice factoring with a non-1 leading coefficient; factor by grouping. |

Solving Quadratic Trinomials by Factoring | Demonstrate how to solve quadratic equations with 3 terms. |

How to Complete the Square | Learn how to complete the square. |

Completing the Square Practice Problems | Get practice completing the square. |

How to Solve a Quadratic Equation by Factoring | Learn how to solve a real life quadratic equation by factoring. |

### 1. Using Tables and Graphs in the Real World

We use tables and graphs in algebra as ways to visually show an equation or function. But do we really use these in the real world? Is it that important to learn about tables and graphs? Find out in this video lesson.

### 2. Scatterplots and Line Graphs: Definitions and Uses

After watching this video, you will be able to understand scatter plots and line graphs. You will also be able to use them to tell people a story about what you see and observe. You will also be able to read them.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 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. 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.

### 11. 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!

### 12. 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!

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### Other Chapters

Other chapters within the Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Linear Equations
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability
- Teacher Resources for High School Algebra