Quadratic Formula Calculator
Solve any quadratic equation ax² + bx + c = 0 using the quadratic formula. Handles real and complex roots, shows the discriminant, and identifies the type of solution.
Inputs
Roots (x values)
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Discriminant (b² − 4ac)
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Vertex of parabola
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Axis of symmetry
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Equation
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About Quadratic Formula Calculator
The formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The ± gives two solutions when the discriminant b² − 4ac is positive.
Discriminant interpretation
b² − 4ac > 0: two distinct real roots (parabola crosses x-axis twice). = 0: one repeated real root (touches x-axis once). < 0: no real roots (parabola misses x-axis), but two complex conjugates exist.
Use cases
Projectile motion (find when something hits the ground), finance (compound-rate solving for time), engineering (resonance, control systems), and optimization problems with quadratic objectives.