# Ch 6: Factoring and Graphing Quadratic Equations: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other precalculus work.
- Identify the quadratic equations concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our Precalculus Tutoring Solution will benefit any student who is trying to learn how to factor and graph quadratic equations to earn better grades. This resource can help students, including those who:

- Struggle with understanding parabolas, the FOIL and area methods, the zero product property or any other quadratic equations topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their quadratic equations unit
- Cope with ADD or ADHD
- Want to get ahead in precalculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning steps for factoring and solving quadratic equations simple and fun.**Cost Efficient**: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality**: Unlike a live precalculus tutor, these video lessons are thoroughly reviewed.**Convenient**: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about quadratic equations on the go!**Learn at Your Pace**: You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Explain what a parabola is and learn how to graph them in standard, intercept and vertex form.
- Factor quadratic equations using the reverse FOIL method.
- Factor polynomials whose leading coefficient is not 1.
- Complete the square.
- Use factoring to solve quadratic equations.
- Solve quadratic equations that have complex numbers as the solution.
- Solve and graph quadratic inequalities.
- Graph systems of quadratic inequalities.
- Apply quadratic functions to simple optimization and motion under gravity problems.
- Model data sets and situations with quadratic functions.

### 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. What is a Function? - Applying the Vertical Line Test

Equations come in all shapes and sizes. Trying to determine which equations are functions can be difficult. You can apply the vertical line test to a graph to quickly tell whether or not it is a function.

### 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. 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. Graphing Circles: Identifying the Formula, Center and Radius

Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.

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### Other Chapters

Other chapters within the Precalculus: Tutoring Solution course

- Functions: Tutoring Solution
- Evaluating Exponential and Logarithmic Functions: Tutoring Solution
- Inequalities: Tutoring Solution
- Foundations and Linear Equations: Tutoring Solution
- Graphing and Rational Equations: Tutoring Solution
- Exponents and Polynomials: Tutoring Solution
- Piecewise and Composite Functions: Tutoring Solution
- Geometry and Trigonometry: Tutoring Solution
- Using Scientific Calculators: Tutoring Solution
- Trigonometry: Tutoring Solution