Solve quadratic equations of the form ax² + bx + c = 0 instantly. Our advanced calculator finds real and complex roots, provides step-by-step solutions, and visualizes the parabola graph with vertex, axis of symmetry, and intercepts.
A quadratic equation is a second-degree polynomial equation in a single variable x with the form:
Where:
The solutions of a quadratic equation are given by the quadratic formula:
The expression under the square root, b² - 4ac, is called the discriminant (Δ).
Two distinct real roots - the parabola crosses the x-axis at two points.
One repeated real root - the parabola touches the x-axis at exactly one point (the vertex).
Two complex conjugate roots - the parabola does not intersect the x-axis.
Input the values for a, b, and c from your equation.
Press the "Solve Equation" button to calculate the roots.
See the solutions, graph, and detailed step-by-step explanation.
Explore vertex, axis of symmetry, and other parabola properties.