Quadratic Equation Calculator

Solve any quadratic equation instantly with this free calculator. Get real and complex roots, discriminant, and vertex coordinates.

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About This Tool

This quadratic equation calculator solves equations of the form ax² + bx + c = 0. Simply enter the coefficients a, b, and c to get instant solutions including real and complex roots, discriminant value, and vertex coordinates of the parabola. The tool provides step-by-step explanations and visualizes the parabola when possible. Perfect for students, teachers, and professionals needing quick quadratic solutions.

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How to Use

Enter the coefficient a (cannot be zero) in the first input field
Enter coefficient b in the second field
Enter constant c in the third field
Click 'Calculate Solutions' to solve the equation
View the roots, discriminant, and vertex in the results section
Use 'Clear Form' to reset all inputs

Frequently Asked Questions

Find Quick Answers

What happens if the discriminant is negative?

The calculator will display complex roots in the form x = p ± qi, where i is the imaginary unit.

Can I solve quadratic equations with a = 0?

No, if a = 0, the equation becomes linear (bx + c = 0), not quadratic. The calculator requires a non-zero value for a.

Does this calculator show the step-by-step solution?

Yes, the calculator displays the discriminant calculation and uses the quadratic formula to find roots with clear explanations.

What information does the vertex provide?

The vertex (h, k) represents the parabola's turning point: h = -b/(2a), k = c - b²/(4a). It shows whether the parabola opens upward or downward.

Need to run multiple calculations?

Create a free account today to unlock unlimited daily runs, access advanced parameters, save your history, and request custom features.

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