Home
#### Algebra and Pre-Algebra Lessons

Algebra 1 | Pre-Algebra | Practice Tests | Algebra Readiness Test
#### Algebra E-Course and Homework Information

Algebra E-course Info | Log In to Algebra E-course | Homework Calculator
#### Formulas and Cheat Sheets

Formulas | Algebra Cheat Sheets

Home » Functions »
Vertex Formula

# Using the Vertex Formula

Quadratic Functions - Lesson 2

## The Vertex Formula

### Given a quadratic function: ax^{2}+ bx + c

### x = -b/2a

## Finding the Vertex

## Example 1

## Practice Problems

### h(x) = 1/2x^{2} - x +2

## Answer Key

# Like This Page?

## Other Function Lessons that You Might Like

Quadratic Functions - Lesson 2

Before we begin this lesson on using the vertex formula, let's briefly recap what we learned in lesson 1.

A quadratic function can be graphed using a table of values. The graph creates a **parabola**. The parabola contains specific points, the vertex, and up to two zeros or x-intercepts. The zeros are the points where the parabola crosses the x-axis.

If the coefficient of the squared term is positive, the parabola opens up. The vertex of this parabola is called the minimum point.

If the coefficient of the squared term is negative, the parabola opens down. The vertex of this parabola is called the maximum point.

In the previous lesson, you graphed quadratic functions using a table of values. In that lesson, I gave you the x values within the table of values.

How would you know which x values to choose if you were graphing a quadratic function on your own? How would you be sure that you chose an x value that allowed you to graph the vertex? This point is essential for graphing a parabola.

There is a special formula that you can use to find the vertex. Once you know the vertex, you can be sure that you have the essential point for graphing the parabola!

Don't forget to check out the *Algebra Class E-courses* if you get confused. There you will find many examples on video and a lot of practice problems.

The following "vertex formula" will give us the x coordinate for the vertex of the parabola.

Now, let's look at an example where we use the vertex formula and a table of values to graph a function.

The vertex, also known as your maximum point, is (-1, 4.5). The zeros of the function are: (-4,0) and (2,0). These are the points where the parabola crosses the x-axis.

Are you having trouble finding the vertex or graphing your homework problems? Use Algebrator Software to graph ANY parabola.

Ok, ready to try one on your own?

Given the following function:

- Predict whether the parabola will open up or down.
- Find the x coordinate of the vertex using the vertex formula.
- Create a table of values and graph the parabola.
- Identify the zeros of function.

Click here to print out graph paper.

Great Job! This concludes our lesson on quadratic functions.

Now you are ready to move onto Step and Discontinuous Functions.

Sign Up for Algebra Class E-courses

Click here to retrieve a lost password.

Custom Search

Most Popular Pages

*"I'd like to start off by relaying my sincerest gratitude for your dedication in teaching algebra. Your methodology is by far the simplest to follow, primarily because you take the time to include the small steps in between that most other teachers leave out.*

*It helps to know why you are doing something. I am 45 and heading to college to get my BS in Business. I need to brush up, hence the visit to your site. Great Job!"*

Jimmy - United States

*"I stumbled onto your site after I found out that I needed to use some fundamental algebra for an assignment. Turns out I had forgotten some things and your great site helped me remember them like "that" (snap of fingers). The organization of the site let me find exactly what I was looking for so easily. Kudos to you for maintaining such a great resource for students of all ages!"*

Tom - United States

*"I just wanted to write and basically thank you for making such a wonderful website! I'm 20 years old and about to take a basic placement test for college. I wanted to brush up on my Algebra skills and I stumbled upon your site. I'm amazed at how simple you make it and how fast I'm remembering Algebra! I don't remember getting most of the answers right when I had an actual teacher in front of me teaching this. Thanks a lot!"*

Elizabeth - United States

*"I am a pensioner living in South Africa. I stumbled on your website, the best thing that could ever happen to me! Your course in Algebra has helped me a lot to better understand the different concepts. Thank you very much for sharing your skills for teaching math to even people like me. Please do not stop, as I am sure that your teachings have helped thousands of people like me all over the world."*

Noel - South Africa

*This is an amazing program. In one weekend I used it to teach my Grade 9 daughter most of the introductory topics in Linear Relations. I took her up to Rate of Change and now she can do her homework by herself.*

Reg - United States

- Algebra Class E-course
- Algebra Class Products
- Print this Site
- Algebra Practice Test
- Algebra Readiness Test
- Homework Answer Calculator
- Practice Worksheets

- Site Map
- Pre-algebra Refresher
- Solving Equations
- Graphing Equations
- Writing Equations
- Systems of Equations
- Inequalities
- Functions
- Exponents & Monomials
- Polynomials
- Quadratic Equations
- Algebra 1 Final Exam

? ## Subscribe To This Site

Then why not use the button below, to add us to your favorite bookmarking service?

Copyright © 2009-2014 Karin Hutchinson ALL RIGHTS RESERVED

## Comments

We would love to hear what you have to say about this page!