Quadratic Formula Calculator
Solve ax2 + bx + c = 0 for real or complex roots. Shows discriminant and vertex.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
Can't find what you need?
Request a ToolHow to Use the Quadratic Formula Calculator
Enter the coefficients a, b, and c from your equation ax2 + bx + c = 0, and the roots appear instantly. No buttons to click.
- Enter coefficient a. This is the number multiplying x2. It cannot be zero (that would be a linear equation, which the tool still solves).
- Enter coefficient b. This is the number multiplying x.
- Enter coefficient c. This is the constant term.
- Read the results. The roots are displayed along with the discriminant, root type, and vertex of the parabola.
About the Quadratic Formula
The quadratic formula x = (-b +/- sqrt(b2 - 4ac)) / (2a) solves any equation of the form ax2 + bx + c = 0. The discriminant (b2 - 4ac) determines the nature of the roots: positive means two distinct real roots, zero means one repeated root, and negative means two complex conjugate roots.
The vertex of the parabola y = ax2 + bx + c is at the point (-b/2a, (4ac - b2)/4a). This is the maximum or minimum point of the quadratic function. All calculations run in your browser with no data sent to any server.
Frequently Asked Questions
What is the discriminant?
The discriminant is b2 - 4ac. If it is positive, the equation has two distinct real roots. If zero, there is one repeated root. If negative, the roots are complex conjugates.
What are complex roots?
When the discriminant is negative, the square root of a negative number appears, producing complex numbers. The roots come in conjugate pairs like 2 + 3i and 2 - 3i, where i is the imaginary unit.
What if a equals zero?
If a = 0, the equation becomes linear (bx + c = 0) with one root: x = -c/b. The calculator handles this case automatically.