Difference between revisions of "Quadratic equation"

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

Revision as of 12:20, 22 April 2007

A quadratic equation can take two forms. The general formula, written as a function of , , is:

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

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

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 is greater than ).

Quadratic equations are very important in calculating the motion of bodies under constant acceleration, i.e., gravity.

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