Solving Quadratic Equations





     This webpage is designed to assist you in solving quadratic equations in a variety of ways.  Some methods can be used at all times while others are only effective for some types of quadratic equations.  You may find it easier to use one method for some equations while other equations can be solved more easily with another method.

The Tasks: 

Review factoring skills that are required when solving quadratic equations by the factoring method.
Solve quadratic equations by factoring.
Solve quadratic equations by completing the square.
Solve quadratic equations using the quadratic formula.

The Resources: 

     Listed below are several sites that will aid you in solving quadratic equations.  Check out these sites for instruction, practice, and review.
1.  Methods Of Factoring - Use this site for a review of factoring quadratic terms.

2.  Solving Quadratic Equations By Factoring - Practice solving quadratic equations by factoring at this site.

3.  Solving Quadratic Equations By Completing The Square - For a review of solving quadratic equations by completing the square, check out this site.

4.  Solving Quadratic Equations Using The Quadratic Formula -  Go here for help on solving quadratic equations with the quadratic formula.

5.  Parabola Guessing Game - This site is a game that helps you visualize translations, reflections, and stretches.

6.  Check Your Answers! - This site allows you to check your solutions for any quadratic equation.
 

The Process: 

1.  Methods Of Factoring - This site reviews some different methods of factoring, including factoring with the Greatest Common Factor (GCF) and factoring trinomials.  These methods must often be applied when solving quadratic equations using the factoring method.  Go to this site and practice these three methods of factoring, and then take the quiz to see how well you understand factoring.

2.  Solving Quadratic Equations By Factoring - Practice solving quadratic equations by factoring at this site.  For a step by step process of the equation you are solving, enter the equation into the blank.  You must use the exponent key (shift + 6) when entering your equation.

3.  Solving Quadratic Equations By Completing The Square - Read a good explanation of the process of solving quadratic equations by completing the square.

4.  Solving Quadratic Equations Using The Quadratic Formula -  Go here for a step by step explanation for solving quadratic equations by using the quadratic formula.

5.  Parabola Guessing Game - This game utilizes the TI-82 calculators and tests your understanding of parabolic translations, reflections, and stretches.  After entering the given program into the calculators, enter guesses for coefficients A and B and the constant term C.  If the result is only one graph instead of two, you win!

6.  Check Your Answers! - After solving a quadratic equation using any method of your choice, check your answers here by entering the coefficients and the constant term of the equation into the appropriate boxes. The Solve button will automatically solve it for you.

7. Quadratics Games! - Test your knowledge of quadratics with a variety of games such as matching, flashcards, and concentration.

Learning Advice: 

     Remember that factoring can only be used when the equation is factorable.  It is generally easier to solve quadratic equations by factoring if they can be factored.  When completing the square, remember to write the equation in the proper form before you begin:  ax² + bx = c.  If you prefer using the quadratic formula, it is highly recommended that you memorize the formula.  You must also be sure to write the equation in the proper form before using the formula:  ax² + bx + c = 0.

Conclusion: 

     Quadratic equations can be solved using different methods.  Factoring can only be used when the equation itself is factorable, but completing the square and the quadratic formula can be used for all quadratic equations.  Most students prefer using the quadratic formula.  What is your favorite method?  Why do you prefer this method?
 
 

     This page originally written by Craig McNatt in Dr. Lewis' EDU 506 class on 6-21-2000.