# Ch 4: Quadratic Equations: College Math Lesson Plans

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### About This Chapter

## Weekly Syllabus

Below is a sample breakdown of the Quadratic Equations chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.

Day | Topics | Key Terms and Concepts Covered |
---|---|---|

Monday | What is a Parabola?; Parabolas in Standard, Intercept and Vertex Form; Multiplying Binomials Using FOIL and the Area Method | The vocabulary for parabolas; Three kinds of quadratic forms; An explanation of methods for multiplying binomials |

Tuesday | Multiplying Binomials Using FOIL and the Area Method: Practice Problems; How to Factor Quadratic Equations: FOIL in Reverse; Factoring Quadratic Equations: Polynomial Problems with a Non-1 Leading Coefficient | Completing practice problems using the FOIL and area methods; The process of factoring quadratic trinomials; The process of reversing the FOIL method |

Wednesday | How to Complete the Square; Completing the Square Practice Problems | An explanation of this process; Transforming a quadratic equation in standard form to one in vertex form |

Thursday | How to Solve a Quadratic Equation by Factoring; How to Use the Quadratic Formula to Solve a Quadratic Equation | Transforming an equation from standard form to intercept form; A review of the steps for using the quadratic formula |

Friday | How to Solve Quadratics That Are Not in Standard Form; Solving Quadratic Inequalities Using Two Binomials | The process of using the distributive and zero product properties; Moving terms within an equation in order to solve quadratic inequalities |

### 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

Other chapters within the College Mathematics Syllabus Resource & Lesson Plans course

- Math Foundations: College Math Lesson Plans
- Linear Equations: College Math Lesson Plans
- Inequalities: College Math Lesson Plans
- Complex & Imaginary Numbers: College Math Lesson Plans
- Properties of Exponents: College Math Lesson Plans
- Properties of Polynomials: College Math Lesson Plans
- Rational Expressions: College Math Lesson Plans
- Properties of Functions: College Math Lesson Plans
- Logarithms & Exponential Equations: College Math Lesson Plans
- Logic: College Math Lesson Plans
- Sets: College Math Lesson Plans
- Probability & Statistics: College Math Lesson Plans
- Geometry: College Math Lesson Plans