# Ch 31: MTEL Mathematics (Elementary): Properties of Quadratic Functions

### About This Chapter

## MTEL Mathematics (Elementary): Properties of Quadratic Functions - Chapter Summary

Make your way through the lessons in this chapter, bettering your ability to work with quadratic equations. You will also review these topics for the exam:

- Using FOIL and the area method to multiply binomials
- Factoring quadratic equations
- Using factoring to solve quadratic trinomials
- The quadratic formula
- Graphing and solving quadratic inequalities
- Parabolas in different forms

Instructors give you the tools to succeed on the exam, and learning doesn't have to be a time-consuming process. The lessons contain video tags, a feature that helps you quickly navigate to certain parts of a lesson. While going through this chapter, use the self-assessment quizzes to gauge your knowledge and skills. This gives you an accurate idea of how prepared you are for the test.

### 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. 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.

### 5. 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!

### 6. 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.

### 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. The Quadratic Formula: Definition & Example

Watch this video lesson to learn how you can use the quadratic formula to solve certain types of problems. Learn what kinds of equations you can solve using this formula as well as how easy it is to use this formula.

### 11. Graphing & Solving Quadratic Inequalities: Examples & Process

When you finish watching this video lesson, you will be able to graph and solve your own quadratic inequality. Learn what steps you need to take and what to watch for.

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### Other Chapters

Other chapters within the MTEL Mathematics (Elementary) (53): Practice & Study Guide course

- MTEL Mathematics (Elementary): Number Sense
- MTEL Mathematics (Elementary): Mathematical Operations
- MTEL Mathematics (Elementary): Factoring & Divisibility
- MTEL Mathematics (Elementary): Real Numbers
- MTEL Mathematics (Elementary): Prime Factorization
- MTEL Mathematics (Elementary): Rational Numbers
- MTEL Mathematics (Elementary): Properties of Numbers
- MTEL Mathematics (Elementary): Roots
- MTEL Mathematics (Elementary): Exponents
- MTEL Mathematics (Elementary): Exponential Expressions & Scientific Notation
- MTEL Mathematics (Elementary): Absolute Value
- MTEL Mathematics (Elementary): Integers
- MTEL Mathematics (Elementary): Estimating & Rounding
- MTEL Mathematics (Elementary): Principles of Fractions
- MTEL Mathematics (Elementary): Operations with Fractions
- MTEL Mathematics (Elementary): Introduction to Decimals
- MTEL Mathematics (Elementary): Operations with Decimals
- MTEL Mathematics (Elementary): Percents
- MTEL Mathematics (Elementary): Descriptive Statistics
- MTEL Mathematics (Elementary): Summarizing Data
- MTEL Mathematics (Elementary): Principles of Sampling
- MTEL Mathematics (Elementary): Regression & Correlation
- MTEL Mathematics (Elementary): Principles of Probability
- MTEL Mathematics (Elementary): Properties of Functions
- MTEL Mathematics (Elementary): Understanding Algebraic Expressions
- MTEL Mathematics (Elementary): Solving Algebraic Equations
- MTEL Mathematics (Elementary): Properties of Linear Relations
- MTEL Mathematics (Elementary): Graphing Linear Equations
- MTEL Mathematics (Elementary): Properties of Ratios & Proportions
- MTEL Mathematics (Elementary): Properties of Polynomial Functions
- MTEL Mathematics (Elementary): Properties of Rational Functions
- MTEL Mathematics (Elementary): Properties of Exponential Functions
- MTEL Mathematics (Elementary): Principles of Measurement
- MTEL Mathematics (Elementary): Principles of Geometry
- MTEL Mathematics (Elementary): Understanding Lines in Geometry
- MTEL Mathematics (Elementary): Principles of Geometric Figures
- MTEL Mathematics (Elementary): Properties of Triangles
- MTEL Mathematics (Elementary): Proof of Theorems
- MTEL Mathematics (Elementary): Quadrilaterals
- MTEL Mathematics (Elementary): Polygons
- MTEL Mathematics (Elementary): Circles & Circular Arcs
- MTEL Mathematics (Elementary): Principles of Geometric Solids
- MTEL Mathematics (Elementary): Parallel Lines & Symmetry
- MTEL Mathematics (Elementary): Transformations in Geometry
- MTEL Mathematics (Elementary): Understanding Coordinate Geometry
- MTEL Mathematics (Elementary School) Flashcards