Quadratic Formula Calculator
Quick answer: Enter a, b, and c to solve ax² + bx + c = 0 and find roots, vertex, and discriminant.
Enter the coefficients a, b, and c of a quadratic equation (ax² + bx + c = 0) to instantly find the roots using the quadratic formula. Shows real or complex roots, the discriminant, vertex coordinates, and axis of symmetry.
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Last reviewed: April 2026Report an error
1x² + -5x + 6 = 0
Roots
x₁ = 3, x₂ = 2
Two real roots: x = 3 and x = 2. Vertex at (2.5, -0.25).
Discriminant (Δ)
1
> 0 · 2 real roots
Vertex X (axis of symmetry)
2.5
Vertex Y
-0.25
Parabola opens
↑ Upward (min)
Parabola y = 1x² + -5x + 6
Parabola crosses x-axis at the two real roots. Opens upward (vertex is the minimum).
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How to Use This Quadratic Calculator
- 1Enter coefficient a (must not be zero).
- 2Enter coefficient b.
- 3Enter coefficient c.
- 4Read the roots (real or complex), discriminant, vertex, and axis of symmetry.
Frequently Asked Questions
- x = (−b ± √(b² − 4ac)) / 2a. The ± means there are two solutions: one using + and one using −.
- If b² − 4ac > 0: two distinct real roots. If = 0: one repeated real root. If < 0: two complex (imaginary) roots — no real x-intercepts.
- The vertex is the turning point: x = −b/2a, y = c − b²/4a. It is the minimum (a > 0) or maximum (a < 0) value of the parabola.
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