# Ch 15: GACE Math: Quadratic Equations

### About This Chapter

## GACE Math: Quadratic Equations - Chapter Summary

These short videos are a fun and convenient method for studying the quadratic equations concepts GACE-certified math educators need to have mastered. As you work through this chapter, you'll cover:

- Different forms of parabolas
- Methods for binomial multiplication
- Factoring quadratic equations
- Completing the square
- Using the quadratic formula to solve equations
- Solving quadratics not in standard form

If you get tripped up on any of the formulas or have questions about the techniques, don't be shy about asking our instructors for help. Make sure to use the lesson quizzes to get an idea of what quadratic equation tasks on the GACE Math assessment might look like.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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!

### 6. 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.

### 7. How to Solve Quadratics with Complex Numbers as the Solution

When you solve a quadratic equation with the quadratic formula and get a negative on the inside of the square root, what do you do? The short answer is that you use an imaginary number. For the longer, more helpful answer, check out this lesson!

### 8. 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.

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### Other Chapters

Other chapters within the GACE Mathematics (522): Practice & Study Guide course

- GACE Math: Properties of Real Numbers
- GACE Math: Fractions
- GACE Math: Decimals & Percents
- GACE Math: Ratios & Proportions
- GACE Math: Measurements & Conversions
- GACE Math: Logic
- GACE Math: Mathematical Reasoning
- GACE Math: Vector Operations
- GACE Math: Matrices & Determinants
- GACE Math: Exponents & Exponential Expressions
- GACE Math: Algebraic Expressions
- GACE Math: Linear Equations
- GACE Math: Inequalities
- GACE Math: Absolute Value Problems
- GACE Math: Polynomials
- GACE Math: Rational Expressions
- GACE Math: Radical Expressions
- GACE Math: Systems of Equations
- GACE Math: Complex Numbers
- GACE Math: Functions
- GACE Math: Piecewise Functions
- GACE Math: Exponential & Logarithmic Functions
- GACE Math: Continuity of Functions
- GACE Math: Limits
- GACE Math: Rate of Change
- GACE Math: Calculating Derivatives & Derivative Rules
- GACE Math: Graphing Derivatives
- GACE Math: Applications of Derivatives
- GACE Math: Area Under the Curve & Integrals
- GACE Math: Integration Techniques
- GACE Math: Integration Applications
- GACE Math: Introduction to Geometric Figures
- GACE Math: Properties of Triangles
- GACE Math: Triangles, Theorems & Proofs
- GACE Math: Parallel Lines & Polygons
- GACE Math: Quadrilaterals
- GACE Math: Circular Arcs & Circles
- GACE Math: Conic Sections
- GACE Math: Geometric Solids
- GACE Math: Analytical Geometry
- GACE Math: Using Trigonometric Functions
- GACE Math: Trigonometric Graphs
- GACE Math: Solving Trigonometric Equations
- GACE Math: Trigonometric Identities
- GACE Math: Sequences & Series
- GACE Math: Graph Theory
- GACE Math: Set Theory
- GACE Math: Overview of Statistics
- GACE Math: Summarizing Data
- GACE Math: Tables & Plots
- GACE Math: Probability
- GACE Math: Discrete Probability Distributions
- GACE Math: Continuous Probability Distributions
- GACE Math: Sampling
- GACE Math: Regression & Correlation
- GACE Mathematics Flashcards