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 x 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>