Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. Get instant results with discriminant analysis, vertex coordinates, and detailed step-by-step solutions.
- Enter the coefficients a, b, and c for ax² + bx + c = 0
- The equation preview and solution update in real-time
- View the discriminant (Δ), roots, vertex, and axis of symmetry
- Follow the step-by-step solution to understand the process
- Quadratic formula — Solves using x = (−b ± √Δ) / 2a
- Discriminant analysis — Shows Δ value and what it means
- Vertex & axis — Displays parabola vertex and axis of symmetry
- Complex roots — Shows complex solutions when Δ < 0
- Step-by-step — Detailed solution breakdown
- What is the quadratic formula?
- x = (−b ± √(b²−4ac)) / 2a — it gives the solutions to any quadratic equation ax² + bx + c = 0.
- What is the discriminant?
- The discriminant Δ = b²−4ac determines the nature of the roots: positive means 2 real roots, zero means 1 double root, negative means complex roots.
- What is the vertex?
- The vertex is the highest or lowest point of the parabola, located at (−b/2a, f(−b/2a)).
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