# Ch 8: Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Quadratic Functions and Equations chapter of your textbook.
- Watch fun videos that cover the quadratic functions and equations you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Formula and samples of quadratic functions
- How to solve, model, graph and transform quadratic functions
- Factoring, graphing or using the formula to solve quadratics
- Definition of zero product property and discriminant
- Solving quadratics in nonstandard form and with complex numbers
- Writing standard form by completing the square
- Applications of quadratic functions
- Using quadratics to solve nonlinear systems

*Explorations in Core Math Algebra 1 is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Quadratic Functions: Examples & Formula

Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.

### 2. Using Quadratic Functions to Model a Given Data Set or Situation

Watch this video lesson to learn how quadratic functions are used to model situations and data gathered from real world scenarios. See how our function fits our data and situation well.

### 3. Quadratics: Equations & Graphs

We will look at quadratic equations: what they are, some forms in which we might find them, how we can put them into standard form, and how their graphs look, including some features of the graphs.

### 4. Graphing Quadratic Functions by Factoring

To graph a quadratic function, it is very helpful to know the zeros of that function. One means of finding the zeros is to factor the function and then use the linear factors to solve for the zeros.

### 5. Transforming Quadratic Functions

The basic form of a quadratic function is f(x)=x^2 . The graph is a parabola with a vertex at (0,0) opening up. All other quadratic functions are transformations of this parent function.

### 6. How to Solve a Quadratic Equation by Graphing

This lesson will show us how to solve a quadratic equation by graphing. Through definitions, illustrations, and applications, we will learn the steps involved in this process.

### 7. 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!

### 8. Zero Product Property: Definition & Examples

After completing this lesson, you will be able to state the Zero Product Property and apply it to real numbers and algebraic expressions. You will also be able to solve equations using the Zero Product Property.

### 9. 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!

### 10. Write the Standard Form of an Equation by Completing the Square

In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.

### 11. 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.

### 12. 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.

### 13. Discriminant: Definition & Explanation

The discriminant helps you to solve quadratic equations. In this lesson, you will learn how to identify the discriminant and how to use it to help you find the number of solutions in a quadratic equation.

### 14. Applying Quadratic Functions to Motion Under Gravity & Simple Optimization Problems

Quadratic functions are very useful in the real world. Watch this video lesson and learn how these functions are used to model real world events such as a falling ball.

### 15. Solving Nonlinear Systems with a Quadratic & a Linear Equation

In this lesson, we'll learn how to solve non-linear systems with a quadratic and linear equation both algebraically and graphically. We'll also look at the different possible solutions for this type of system.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 1: Equations
- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 3: Functions
- Explorations in Core Math Algebra 1 Chapter 4: Linear Functions
- Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities
- Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis