Quadratic equation

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

<math>y = ax^2 + bx + c</math>

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

The points where this curve crosses the y axis are represented by the second form of the equation:

<math>ax^2 + bx + c = 0</math>

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 <math>4ac</math> is greater than <math>b^2</math>).

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:

<math>\frac{dy}{dx} = 2ax + b</math>