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 »
Quadratic Functions

# Quadratic Functions - Lesson 1

### f(x) = ax^{2} +bx + c

## Example 1

## Practice Problem

## f(x) = -x^{2} -6x -1

## Answer Key

## Can you guess which factor in the function determines whether the parabola opens up or down?

### fx) = ax^{2} +bx+c

# Like This Page?

## Other Function Lessons that You Might Like

So far in our study of Algebra, we have discovered all of the ins and outs of linear equations and functions. We know that linear equations graph a straight line, so I wonder what a **quadratic** function is going to look like?

Let's take a look!

A quadratic function is always written as:

Ok.. let's take a look at the graph of a quadratic function, and define a few new vocabulary words that are associated with quadratics.

- The graph of a quadratic function is called a
**parabola**. A parabola contains a point called a**vertex**. The parabola can open up or down. - If the parabola opens up, the vertex is the lowest point. This point is called the
**minimum point**. - If the parabola opens down, the vertex is the highest point. This point is called the
**maximum point** - A parabola also contains two points called the
**zeros**or some people call these the x-intercepts. The zeros are the points were the parabola crosses the x-axis.

Now, we will use a table of values to graph a quadratic function. Remember that you can use a table of values to graph any equation.

There are a few tricks when graphing quadratic functions. We must make sure that we find a point for the vertex and a few points on each side of the vertex.

Notice that after graphing the function, you can identify the vertex as (3,-4) and the zeros as (1,0) and (5,0).

So, it's pretty easy to graph a quadratic function using a table of values, right? It's just a matter of substituting values for x into the equation in order to create ordered pairs.

There are a lot of other cool things about quadratic functions and graphs. Locate the vertex on the completed table of values. Do you notice any patterns? Look specifically at the f(x) values.

Notice how the f(x) values start to repeat after the vertex? Quadratic functions are symmetrical. If you drawn an imaginary line through the vertex, this is called the **axis of symmetry**.

Now check out the points on each side of the axis of symmetry. Pretty cool, huh?

Directions: Use the table of values to graph the following function:

Then identify the vertex of the function.

Click here to print out graph paper.

Notice that the zeros of the function are not identifiable on the graph. (They contain decimals which we can not accurately read on this graph).

The vertex for the parabola is (-3,8).

This parabola opens down; therefore the vertex is called the **maximum point.**

It's the sign of the first term (the squared term). In the function:

If a is positive the parabola opens up and the vertex is the minimum point.

If a is negative, the parabola opens down and the vertex is the maximum point.

For more help with quadratic functions, see lesson 2 on quadratics.

- Introduction to Relations
- Identifying Functions &

Using the Vertical Line Test - Function Notation
- Evaluating Functions
- Linear Functions - Part 1
- Linear Functions - Part 2
- Quadratic Functions -

Part 2 - Using the Vertex Formula - 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
- 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!