# Quadratic equation

### From Conservapedia

A **quadratic equation** can take two forms. The general formula, written as a function of *x*, *y* = *f*(*x*), is:

*y*=*a**x*^{2}+*b**x*+*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:

*a**x*^{2}+*b**x*+*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 4*a**c* is greater than *b*^{2}).

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:

## Factoring

Quadratic equations can be simplified by factoring it into (*x* + *r*)(*x* + *s*), where *r* + *s* equals B in *y* = *x*^{2} + *b**x* + *c* and *r**s* 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 *a**x*^{2} + *b**x* into *a*(*x*^{2} + *b* / *a**x*). This works because both *x*^{2} and *b**x* were divided by *a*, which was put back later via multiplication.