Quadratic Formula Derivation


Given a quadratic equation with one variable where the variable and the parameters are from the domain of real numbers.


        A.  The usual process is one of "completing the square."   Although all of these are somewhat similar, find at least 4 sequences of completing the square to arrive at the Quadratic Formula.

         1.  Begin by transforming to 

2.  Begin by transforming to 

3.  Begin by transforming to

4.  Begin by transforming to

Although all four of these derivations are very similar, it may be worth thought and discussion as to which derivation is easiest to understand.

Do students need to understand the derivation?   Will it be on any assessment they encounter?

When should the derivation be taught?

Do mathematics teachers need to understand the derivation?


See the Alternative Quadratic Formula.     This form has useful application in some areas of computer science.      Explore examples with it enough to be fully convinced that it works.