How to use Quadratic Equation Solver
- Enter a, b and c for the equation ax² + bx + c = 0.
- Read the discriminant and the roots.
- Use the vertex to sketch the parabola.
About this tool
The solutions come from the quadratic formula x = (-b ± sqrt(b² - 4ac)) / 2a. The part under the root is the discriminant: positive gives two real roots, zero gives one repeated root and negative gives two complex roots.
The vertex of the parabola is at x = -b / 2a, which is where the function reaches its minimum (a > 0) or maximum (a < 0).
Frequently Asked Questions
- What if a is 0?
- Then the equation is linear, not quadratic, and has the single solution x = -c / b.
- What are complex roots?
- When the discriminant is negative the solutions involve the imaginary unit i, and the parabola does not cross the x-axis.
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