Quadratic Equation Solver
See roots, discriminant, and vertex from coefficients
係数を入力
1x² + -3x + 2 = 0
計算結果
About Quadratic Equation Solver
Understanding quadratic equations requires seeing not only the roots but also how the discriminant determines the type of solution and the parabola's key features (vertex and axis of symmetry).
This calculator takes the three coefficients a, b, and c and instantly displays the roots using the quadratic formula, identifies whether you have two distinct real roots, a double root, or complex roots, and calculates the vertex and axis of symmetry simultaneously. The discriminant D = b² - 4ac automatically determines the solution type, and the tool computes the parabola's vertex (h, k) and symmetry axis x = h.
When a = 0, the tool switches to linear equation mode; when b = 0, it handles the constant case (identity or no solution). Perfect for homework review, classroom demonstrations, exam preparation, university entrance exams, and quick coefficient verification in professional contexts.
How to use Quadratic Equation Solver
- Enter the coefficients a, b, c from your equation y = ax² + bx + c into the input boxes.
- The equation preview updates automatically; the default example shows a=1, b=-3, c=2.
- Click Solve to calculate and display x1, x2, the discriminant, the axis of symmetry, and the vertex.
- Compare the discriminant value with the solution type to visualize whether the parabola crosses the x-axis twice, touches it, or doesn't touch it at all.
Benefits of Quadratic Equation Solver
- Seeing the discriminant value and solution type together helps you predict the parabola's behavior (two real roots ⟹ crosses x-axis twice; double root ⟹ touches; complex roots ⟹ doesn't cross).
- The axis of symmetry and vertex are displayed side by side, making parabola sketching and applied problems much easier.
- Automatically handles edge cases like a = 0 (linear) and b = 0 (constant), making it perfect for validating coefficients and avoiding input errors.
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