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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 section]]s. (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 number|real]] roots, but result in the [[imaginary number|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]].
The [[derivative]] of a quadratic equation is a simple [[linear function]]:
:<math>\frac{dy}{dx} = 2ax + b</math>
:<math>y = ax^2 + bx + c</math>
The graph of a quadratic equation is a [[parabola]], one of the [[conic section]]s. (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 number|real]] roots, but result in the [[imaginary number|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]].
The [[derivative]] of a quadratic equation is a simple [[linear function]]:
:<math>\frac{dy}{dx} = 2ax + b</math>