Quadratic equation

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

$y=ax^{2}+bx+c$

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 y axis are represented by the second form of the equation:

$ax^{2}+bx+c=0$

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 $b^{2}$).

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:

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