Quadratic Equation Calculator
Solve ax² + bx + c = 0 step by step. Get real or complex roots, discriminant, vertex, axis of symmetry, and parabola graph.
Enter coefficients Quadratic formula
1x² + 0x + 0 = 0
a (x² coefficient)
x² +
b (x coefficient)
x +
c (constant)
= 0
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Discriminant (b²−4ac)
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Vertex (h, k)
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Axis of symmetry
FAQs
What is the quadratic formula? ›
The quadratic formula solves ax² + bx + c = 0: x = (−b ± √(b²−4ac)) / 2a. The ± gives two solutions. The discriminant (b²−4ac) determines the nature of roots: if positive → two distinct real roots; if zero → one repeated real root; if negative → two complex conjugate roots (no real solutions). The formula works for any quadratic equation where a ≠ 0.
What is the discriminant? ›
The discriminant is b² − 4ac. It tells you the type of roots without solving: Positive → two different real roots (parabola crosses x-axis twice); Zero → exactly one real root (parabola just touches x-axis); Negative → two complex roots (parabola doesn't cross x-axis). A positive perfect-square discriminant means the equation can also be solved by factoring.