Goodness Gracious, Quadratic Functions!

Click the title for a musical rendition to "Great Balls of Fire."

 

a WebQuest for grades 9-12 Algebra

by Shelli Brasher

Introduction | Task | Resources | Process | Evaluation | Conclusion

Introduction

Why study quadratics? There are many ways to solve a problem. Some are more efficient than others.

To design a supersonic aircraft, an engineer must select a design method that completes the job quickly and efficiently. Quadratic equations can be solved using several methods. The idea is to master these methods and learn to select the one that most efficiently solves the problem at hand.

 

Also, the parabola, the graph of a quadratic, has numerous applications in the modern world of technology. Supersonic planes are parabolic in shape to reduce air resistance.

Flashlights and satellite dish antennas have reflectors shaped like a parabola.

Even the graph showing how a golf ball rises until it reaches its maximum height, then falls back to earth is shown by a parabola.


The Task

 In this WebQuest, you will use a variety of resources to

  • investigate the various methods of solving quadratic equations, which include factoring, substitution, elimination, completing the square, graphing, and using the quadratic formula,
  • examine the characteristics of the graph of a parabola and determine how these characteristics relate to the quadratic equation,
  • discover various real world applications, and
  • develop some guidelines for determining the most efficient method to use to solve the problems posed in these applications.


Resources

 

There are literally millions of sources at your fingertips that will help you with this task. The World Wide Web offers a multitude of excellent sites pertaining to quadratic functions and their applications. Some recommended sites are:

Search Engines:

  • Yahoo - Search engine that has listings of topics
  • Yahooligan - Search engine for kids that has topic listings

 

Math Sites:

 


The Process

  1. First you'll select a partner. Be wise in your selection. Choose someone you can depend on to work diligently and do their fair share of the work.
  2. Next, put on your swimsuit and let's go surfing!Well, not really! Instead, for the next 45 minutes "surf" the links that are listed in the resources section. Look specifically for content related to "quadratics". As you search, keep a journal of where you go and what you find at that site.
  3. Now, back to the real world. Complete the assignments in your textbook dealing with solving quadratics. (You don't need your partner for this part!) Use the specified timeline for completion. Your journal can be used to help you find answers to any questions you may have.
  4. Finally, the best for last. Grab your partner and journey to the best Math site ever, called  Logal. Here you will experience the following simulations. Record your answers for each activity on your own paper to turn in.

     


Evaluation

At the end of this unit of study, you will submit a portfolio of your work and findings which pertain to quadratic functions. View the portfolio checklist for a complete listing of works to be included and their grade values.


Conclusion

Now, you should feel like a quadratic expert! You can recognize a quadratic function, determine the best method to use to solve it, analyze its graph, and (most important) use quadratic functions to solve other problems! CONGRATS!

 

I'd love to know how you felt about these activities, including any problems you may have had as well as your successes. I look forward to hearing from you!

 

Last updated June 24, 1999

Based on a template from The WebQuest Page.