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(x) = ax2 + bx + c , with a0

A quadratic equation is a quadratic function that is equated to 0. It has the general form:

ax2 + bx + c = 0 , with a0

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.

x2
+
x
+
=0

Please report any error to [email protected]



Properties of quadratic functions and quadratic equations:

  • Parabola of a quadratic function The graph of a quadratic function 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 the function at the axis of symmetry, i.e. evaluating f(x) at x = 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.

      Parabola opening up and parabola opening down
  • The value of b2 4ac is called the Discriminant (D or Δ) 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.

    Three types of parabola depending on discriminant value

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