Introduction

This lesson was developed as a part of the Vanguard for Technology Integration (K-12) research group funded by the Moffat County School District RE:1.
This lesson will assist students in solving quadratic equations through the use of the quadratic formula.

Learners

This concept is begun in Algebra 1 and further explored in Algebra 2.  Quadratic equations will also be encountered in Chemistry, Physics, Electricity,  Business and Marketing.
A student will need to have a basic knowledge in common algebraic concepts as well as a working knowledge of radicals, multiplying binomials, and solving both fractional and linear equations before attempting this lesson.
 

Curriculum Standards

The K-12 math standards articulate five general goals for all students: 

         1.that they learn to value mathematics 
         2.that they become confident in their ability to do mathematics
         3.that they become mathematical problem solvers 
         4.that they learn to communicate mathematically 
         5.that they learn to reason mathematically 

Specific Moffat County High School Curriculum Standard addressed:

• be able to use the quadratic formula to solve a quadratic equation 

To solve quadratic equations by use of the formula you must first get the equation in the form of:
                        ax2  + bx + c = 0

Where a, b and c are constants and c cannot equal 0.  Then a, b, and c can be in any form (integers, fractions, decimals, etc.).  However, it is generally easier to work with if the numbers are all integers and even better if a is positive. 

    Once the quadratic equation is in the form above then the formula used to solve for x is as follows: 

    Therefore, just plug the numbers for a, b, and c (the coefficients of the squared term, the linear term, and the constant) into the formula and simplify.

    One of the two places to be especially careful when simplifying is to take the opposite of b.  In other words, the number in the formula is not always negative but is the opposite sign of whatever b is.  The second place, and possibly of even more concern is the minus 4ac.  If 4ac turns out to be a negative number then you will be taking the opposite of that and adding to b squared rather than subtracting.

 If exact answers are desired, just simplify the radical as is necessary and leave it as part of the answer.  If approximations are needed then find the decimal approximation for the radical and add or subtract from the opposite of b.  Of course, as with all quadratic equations, there will be two solutions.  The plus or minus in front of the radical sign is what brings us the two roots.  If you get a negative number under the radical sign there will be two imaginary answers.  If you have not studied imaginary numbers at this time then your answer would be no real solutions.
 

     Now it is time to see if what we have discussed makes any sense. 
     Here are a few practice problems to see how well you understand the concept. 
     The first group in Task 1 has all of the equations in the correct form and equal 
      to zero. 
     The second group in Task 2 requires that you get the equation into the 
    ax2  + bx + c = 0 form first before using the quadratic formula.

Upon completion of each of the first three tasks listed below click on the button that follows the problems, then on Task 4 be sure to use the BACK button on your browser to return to the home page.  Task 4 is an optional link to a web site that allows you more opportunity to practice the quadratic formula.

• Task 1
• Task 2
• Task 3

Task 4

Resources Needed
 
 

• Class sets of Algebra books 
• Netscape 5.0
• Appleworks 4.7 
• Printer
• possibly Chemistry Text if working in that curriculum area
• Calculator if not computer not equiped with one

Evaluation

The student will be given 10 problems to do on their own.  Eight of them are equations and two are word problems.  Upon completion of all ten, they will  compare their answers to those provided and see how they did.   If they did not get at least 7 correct they might  need some more practice.  Anything above 8 and they have probably mastered the quadratic formula. 
Evaluation Tasks

Conclusion

By mastering the quadratic formula students will not only excel in Algebra but will be able to transfer this information into various other studies such as chemistry and physics correctly, and with ease.

Credits & References

Houghton Mifflin Algebra 1 
Houghton Mifflin Algebra 2 & Trigonometry