A quadratic equation can take two forms. The general formula, written as a function of , , is:
The points where this curve crosses the x axis are represented by the second form of the equation:
These are solved for using the quadratic formula, which will not only solve for real roots, but result in the imaginary roots if the parabola does not actually cross the y axis (this is when is greater than ).
Quadratic equations can be simplified by factoring it into , where equals B in and equals in the above equation. Equations that cannot be easily factored this way can become easy to factor by completing the square.
If the coefficient of X is not one
If the coefficient of X is not 1, then one can turn into . This works because both and were divided by , which was put back later via multiplication.