Solve ax² + bx + c = 0 using the quadratic formula. Finds real and complex roots, discriminant, vertex, and axis of symmetry.
Enter coefficients for ax² + bx + c = 0
| Formula | Expression |
|---|---|
| Roots | x = (−b ± √(b²−4ac)) / 2a |
| Discriminant | Δ = b² − 4ac |
| Vertex x (h) | h = −b / 2a |
| Vertex y (k) | k = c − b²/4a |
| Sum of roots | x₁ + x₂ = −b/a |
| Product of roots | x₁ · x₂ = c/a |
| Property | Value |
|---|---|
| x₁ | 3 |
| x₂ | 2 |
| Discriminant (Δ) | 1 |
| Vertex (h, k) | (2.5, -0.25) |
| Axis of symmetry | x = 2.5 |
| y-intercept | (0, 6) |
| Parabola opens | Upward ↑ (minimum at vertex) |
| Δ | Roots | Graph |
|---|---|---|
| Δ > 0 | Two distinct real roots | Crosses x-axis twice |
| Δ = 0 | One repeated real root | Touches x-axis once |
| Δ < 0 | Two complex conjugate roots | Never crosses x-axis |