# Ch 18: CEOE Middle Level/Intermediate Math: Quadratic Functions

### About This Chapter

## CEOE Middle Level/Intermediate Math: Quadratic Functions - Chapter Summary

We have prepared this series of lessons as a refresher before you take the CEOE Middle Level/Intermediate Math test. They will help you answer exam questions about quadratic functions covering subject matter including:

- The definition of a parabola
- How to use the parabola in standard, intercept and vertex form
- The equation and formulas for finding the axis of symmetry
- Using FOIL and the area method for multiplying binomials
- Using FOIL in reverse for factoring quadratic equations
- Polynomial problems having non-1 leading coefficients and factoring quadratic equations
- Use of factoring for solving quadratic trinomials
- Completing the square
- The definition of the quadratic formula
- Understanding nonlinear equations in two variables
- The process of solving and graphing quadratic inequalities

The video lessons are divided into short, manageable segments. After both the text and video lessons, you can take a quiz to check your comprehension. With the videos, you can easily go back and review specific information by using our handy, keyword-based timeline tool.

### 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. Find the Axis Of Symmetry: Equation, Formula & Vertex

This lesson discusses how to locate the axis of symmetry of a parabola in the standard x-y coordinate plane. Learn how the vertex of the parabola relates to its axis of symmetry and how to determine the axis of symmetry from a quadratic equation.

### 4. 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.

### 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. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 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.

### 12. Graphing a System of Quadratic Inequalities: Examples & Process

What is a system of quadratic inequalities? What are the steps to graphing them? Find the answers to these questions by watching this video lesson. When you finish, you will be able to graph these yourself.

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### Other Chapters

Other chapters within the OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

- CEOE Middle Level/Intermediate Math: Problem Solving Strategies
- CEOE Middle Level/Intermediate Math: Reasoning & Logic
- CEOE Middle Level/Intermediate Math: Mathematical Modeling
- CEOE Middle Level/Intermediate Math: Real Numbers
- CEOE Middle Level/Intermediate Math: Fractions
- CEOE Middle Level/Intermediate Math: Decimals
- CEOE Middle Level/Intermediate Math: Percentages
- CEOE Middle Level/Intermediate Math: Ratios, Rates & Proportions
- CEOE Middle Level/Intermediate Math: Exponents & Exponential Expressions
- CEOE Middle Level/Intermediate Math: Properties of Real Numbers
- CEOE Middle Level/Intermediate Math: Sequences & Series
- CEOE Middle Level/Intermediate Math: Introduction to Algebra
- CEOE Middle Level/Intermediate Math: Introduction to Functions
- CEOE Middle Level/Intermediate Math: Linear Equations
- CEOE Middle Level/Intermediate Math: Linear Inequalities
- CEOE Middle Level/Intermediate Math: Systems of Equations
- CEOE Middle Level/Intermediate Math: Matrices in Linear Algebra
- CEOE Middle Level/Intermediate Math: Polynomial Functions
- CEOE Middle Level/Intermediate Math: Rational Expressions
- CEOE Middle Level/Intermediate Math: Radical Expressions
- CEOE Middle Level/Intermediate Math: Absolute Value Functions
- CEOE Middle Level/Intermediate Math: Exponential & Logarithmic Equations
- CEOE Middle Level/Intermediate Math: Measurement
- CEOE Middle Level/Intermediate Math: Area & Perimeter
- CEOE Middle Level/Intermediate Math: Surface Area & Volume
- CEOE Middle Level/Intermediate Math: Foundations of Geometry
- CEOE Middle Level/Intermediate Math: Lines & Angles
- CEOE Middle Level/Intermediate Math: Properties of Triangles
- CEOE Middle Level/Intermediate Math: Similar & Congruent Triangle Proofs
- CEOE Middle Level/Intermediate Math: Right Triangle Proofs
- CEOE Middle Level/Intermediate Math: Quadrilaterals & Polygons
- CEOE Middle Level/Intermediate Math: Circles & Arc of a Circle
- CEOE Middle Level/Intermediate Math: Conic Sections
- CEOE Middle Level/Intermediate Math: Coordinate Geometry
- CEOE Middle Level/Intermediate Math: Transformations in Geometry
- CEOE Middle Level/Intermediate Math: Trigonometry
- CEOE Middle Level/Intermediate Math: Limits
- CEOE Middle Level/Intermediate Math: Rate of Change & Derivatives
- CEOE Middle Level/Intermediate Math: Area Under the Curve & Integrals
- CEOE Middle Level/Intermediate Math: Probability
- CEOE Middle Level/Intermediate Math: Discrete Probability Distributions
- CEOE Middle Level/Intermediate Math: Continuous Probability Distributions
- CEOE Middle Level/Intermediate Math: Overview of Statistics
- CEOE Middle Level/Intermediate Math: Sampling
- CEOE Middle Level/Intermediate Math: Graphs, Charts & Diagrams
- CEOE Middle Level/Intermediate Math: Summarizing Data
- CEOE Middle Level/Intermediate Math: Discrete Mathematics
- OSAT Middle Level/Intermediate Mathematics (CEOE) (125) Flashcards