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Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0 instantly. Finds real and complex roots, discriminant, vertex, and axis of symmetry with step-by-step solutions.
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Enter coefficients for ax² + bx + c = 0
Key Features — Quadratic Formula Calculator
Solves ax² + bx + c = 0 for any coefficients
Handles real and complex roots
Discriminant with nature of roots
Vertex and axis of symmetry
Step-by-step solution shown
Parabola direction indicated
Why Use This Tool — Quadratic Formula Calculator
Free Online Quadratic formula calculatorQuadratic equation solver — for EveryoneFast & Easy Solve quadratic equationQuadratic formula — 100% FreeFree Online Discriminant calculator
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Frequently Asked Questions — Quadratic Formula Calculator
What is the quadratic formula?
The quadratic formula solves ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) / 2a. The discriminant b² − 4ac determines the nature of roots: positive = two real roots, zero = one repeated root, negative = two complex roots.
What does the discriminant tell you?
The discriminant (Δ = b² − 4ac) reveals the number and type of solutions. If Δ > 0: two distinct real roots. If Δ = 0: one real root (the parabola touches the x-axis). If Δ < 0: two complex conjugate roots (the parabola does not cross the x-axis).
How do I find the vertex of a parabola?
The vertex is at (h, k) where h = −b/(2a) and k = c − b²/(4a). The axis of symmetry is the vertical line x = h. The vertex is the minimum point if a > 0 (parabola opens up) and maximum if a < 0 (opens down).