See also: numbers
A quadratic equation is a second degree polynomial equation. It has the general form:
$$a{x}^{2}+bx+c=0\text{, with}\phantom{\rule{10px}{0ex}}a\ne 0$$
The calculator below will calculate the Discriminant ($D$) and find the solutions (roots) of a quadratic equation.
Quadratic Equation Calculator
Enter the values of the coefficients a, b, and c.
Please report any error to [email protected]
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
$x=\frac{b}{2a}$
.
 The coordinate of the vertex of the parabola is found by evaluating $y$ at the axis of symmetry, i.e.
evaluating $y$ at
$x=\frac{b}{2a}$
.
 If $a>0$ (i.e. positive), the parabola of the equation will face (open) up.
If $a<0$ (i.e. negative), the parabola of the equation will face (open) down.
 The value of
${b}^{2}4ac$
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.
By Jimmy Sie
See also: numbers