A quadratic equation can take two forms. The general formula, written as a function of x, y = f(x), is:
- y = ax2 + bx + c
The points where this curve crosses the x axis are represented by the second form of the equation:
- ax2 + bx + c = 0
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 4ac is greater than b2).
Quadratic equations can be simplified by factoring it into (x + r)(x + s), where r + s equals B in y = x2 + bx + c and rs equals c 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 ax2 + bx into a(x2 + b / ax). This works because both x2 and bx were divided by a, which was put back later via multiplication.