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The quadratic formula is used to simplify the process of solving a quadratic equation. It is in the following form:

The '''quadratic formula''' is used to simplify the process of solving a [[quadratic equation]].  

:<math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}</math>

First, the quadratic  equation must be reduced to this format:

:<math>ax^2+bx+c=0\!</math>

:<math>ax^2+bx+c=0\!</math>

You simply substitute <math>a</math>, <math>b</math>, and <math>c</math> into the formula.

Then the coefficients ''a'', ''b'', and ''c'' can be substituted in the formula to find the solutions:

 

:<math>x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}</math>

 

You can prove that the formula is correct by substituting the formula in place of '''x''' in <math>ax^2+bx+c=0\!</math> and then gradually simplifying the rather complicated formula that results, step by step.  Eventually, if all the steps are done correctly, it will simplify to 0.

You can prove that the formula is correct by substituting the formula in place of '''x''' in <math>ax^2+bx+c=0\!</math> and then gradually simplifying the rather complicated formula that results, step by step.  Eventually, if all the simplifying steps are done correctly, it will simplify to 0.  Derivation of the formula is usually done via the method of completing the square.

Derivation of the formula is usually done via the method of [[completing the square]].

[[Category:Mathematics]]

[[Category:Mathematics]]