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 graph of a quadratic equation is a parabola, one of the conic sections. (In some cases, the parabola collapses, most obviously when a = 0)

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 are very important in calculating the motion of bodies under constant acceleration, i.e., gravity (when close to the earth's surface).

The derivative of a quadratic equation is a simple linear function:

$\frac{dy}{dx} = 2ax + b$

## Factoring

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.[1] 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.