Quadratic Equation Calculator
Solve any quadratic equation ax² + bx + c = 0 and see the steps, vertex and graph.
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Solutions
- Roots
- Discriminant
- Vertex
- Factored form
- Sum and product of roots
- Work
Saved Calculations
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The Quadratic Formula
x = (−b ± √(b² − 4ac)) ÷ 2a
The discriminant b² − 4ac tells you the kind of roots: positive gives two real roots, zero gives one repeated root, negative gives two complex roots. The vertex of the parabola is at x = −b ÷ 2a.
Worked Example
Tips
Check your answer by plugging a root back in: 5² − 3(5) − 10 = 0. The roots add up to −b/a and multiply to c/a.