See also: Quadratic Equation Factorisation, Quadratic Equation Formula,
Quadratic Equation Completing the Square, numbers
A quadratic function is a function defined by a second degree polynomial. It has the general form:
$$f\left(x\right)=a{x}^{2}+bx+c\text{, with}\phantom{\rule{10px}{0ex}}a\ne 0$$
A quadratic equation is a quadratic function that is equated to $0$.
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 quadratic functions and quadratic equations:

The graph of a quadratic function 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 the function at the axis of symmetry, i.e.
evaluating $f\left(x\right)$ at
$x=\frac{b}{2a}$
.
 If $a>0$ (i.e. positive), the parabola of the function will face (open) up.
If $a<0$ (i.e. negative), the parabola of the function will face (open) down.
 The value of
${b}^{2}4ac$
is called the Discriminant ($D$ or $\Delta $) of the quadratic equation.
By looking at the value of the discriminant of a quadratic equation, we can know the following:
 If the discriminant is positive ($D>0$), the quadratic equation has 2 distinct roots and both are real numbers.
The parabola of the quadratic function intercepts the $x$axis 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 function intercepts the $x$axis 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 function does not intercept the $x$axis.
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: Quadratic Equation Factorisation, Quadratic Equation Formula,
Quadratic Equation Completing the Square, numbers
See also: numbers