What This Calculator Does

The Quadratic Equation Calculator solves the standard form ax^2 + bx + c = 0. Enter the three coefficients and the page applies the quadratic formula, then places the discriminant, root type, axis of symmetry, and vertex beside the roots. That gives you more than two decimals: it tells you whether real solutions exist and how the corresponding parabola is positioned.

It works well for homework checking, classroom review, graph intuition, and quick numeric inspection. A positive discriminant means two x-intercepts, zero means the parabola touches the x-axis at its vertex, and a negative discriminant means no real x-intercepts and a conjugate pair of complex roots. This is a numeric tool, not a symbolic simplifier, radical reducer, or graphing application.

For a more general equation with variables, use the Equation Solver. To evaluate a numeric expression before you extract coefficients, use the Mathematical Expression Calculator. For keypad-based trig, logarithm, and power work, see the Scientific Calculator.

When to Use It

• You want to solve a quadratic equation quickly.
• You want to know whether it has two real roots, one repeated root, or complex roots.
• You want the axis of symmetry and vertex as well as the roots.
• You want to check the number of x-intercepts and the parabola's turning point together.
• You are checking homework, review exercises, or a simple model.
• You want numeric approximations from coefficients without substituting into the formula by hand.

Inputs Explained

The three coefficients a, b, and c

These are the coefficients in ax^2 + bx + c = 0. a must be nonzero; if a=0, the highest degree drops to one and the page reports an error. b and c may be zero, for example x^2-4=0 uses a=1,b=0,c=-4.

The fields accept ordinary decimal input such as -3, 0.5, .25, or 3.. They do not parse variables, units, commas, text scientific notation such as 1e3, or expressions such as 2+3; first rearrange the original equation into numeric coefficients.