See also: numbers
A quadratic equation is a second degree polynomial equation. It has the general form:
The calculator below will calculate the Discriminant () 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
.
- The coordinate of the vertex of the parabola is found by evaluating at the axis of symmetry, i.e.
evaluating at
.
- If (i.e. positive), the parabola of the equation will face (open) up.
If (i.e. negative), the parabola of the equation will face (open) down.
- The value of
is called the Discriminant () 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 (), the quadratic equation has 2 distinct roots and both are real numbers.
The parabola of the quadratic equation intercepts the x-axis at two points.
- If the discriminant is equal to zero (), the quadratic equation has 1 root and it is a real number.
The parabola of the quadratic equation intercepts the x-axis at exactly one point.
- If the discriminant is negative (), the quadratic equation has 2 distinct roots and both are complex numbers.
The parabola of the quadratic equation 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: numbers