Quadratic Equations
See also: numbers
A quadratic equation is a second degree polynomial equation. It has the general form:
0 = ax² + bx + c, with a ≠ 0
Calculator
The calculator below will give calculate the Discriminant and find the solutions (roots) of a quadratic equation (function).
Please report any error to [email protected]. Thank you.
Properties of a quadratic equation:

The graph of a quadratic equation is called a parabola.
 The axis of symmetry of the parabola is the line x = ^{b}/_{2a}.
 The coordinate of the vertex of the parabola is found by evaluating y at the axis of symmetry, i.e. evaluating y at x = ^{b}/_{2a}.
 If a > 0 (i.e. positive), the parabola of the equation will face (open) up,
if If a < 0 (i.e. negative), the parabola of the equation will face (open) down.
 The value of b² − 4ac is called the Discriminant (D) of the quadratic equation.
By looking at the value of the discriminant of a quadratic equation, we can know the following:
 If the discriminant is positive (D > 0), the quadratic equation has 2 distinct roots and both are real numbers. The parabola of the quadratic equation intercepts the xaxis at two points.
 If the discriminant is equal to zero (D = 0), the quadratic equation has 1 root and it is a real number. The parabola of the quadratic equation intercepts the xaxis at exactly one point.
 If the discriminant is negative (D < 0), the quadratic equation has 2 distinct roots and both are complex numbers. The parabola of the quadratic equation does not intercept the xaxis.
Methods to solve or find the roots of a quadratic equation
There are a few methods to solve a quadratic equation, other than using the calculator above. The following are some of them.
 Factorization
 Completing the square
 Formula
See also: numbers