aX2 + bx + c
In mathematics, a quadratic equation is defined as any equation taking the form of:
aX2 + bX + c
where X is an unknown quantity and a, b, and c are constants such that a does not equal zero. Since these equations contain only one true unknown (we solve for a, b, and c during the course of our analysis), they are referred to as univariate equations. They are considered second degree polynomials since their highest power is two (raising X to a square). Solving these equations occurs via a process known as factoring (to Americans) or factorising (elsewhere).
This calculator finds the solutions to this equation, in the form of:
If these two parts of multipled together algebraically, they will create the original equation. These two solutions are referred to as the roots of the quadratic equation. If plotted on a graph, these are the x-values at which the resulting parabola will cross the x-axis of the graph.
As well as being a formula that will yield the zeros of any parabola, the quadratic formula gives the axis of symmetry of the parabola, and it can be used to determine how many real zeros exist for that equation. The axis of symmetry is expressed as the line x = -b/2a (these being the co-efficients of the original equation).
From a historical perspective, quadratic equations are a relatively old branch of mathematics. They were important to solving problems related to the area and sides of rectangles. Early solutions to these problems were geometric in nature. Algebraic solutions emerged around 700 A.D. The modern form of the quadratic equation was published in 1637 by Rene Descartes. This calculator is based on a digital version of that approach.