Solve quadratic equations using the quadratic formula with step-by-step solutions and graphical visualization.
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Embed this quadratic equation solver on your website for free. It's responsive, always up-to-date, and easy to customize.
Enter coefficients and click "Solve & Analyze Equation" to see comprehensive mathematical analysis.
Solve ax² + bx + c = 0 and analyze parabolas with multiple methods and clear outputs.
Provide a, b, c for ax² + bx + c = 0.
Get roots and discriminant instantly.
See vertex, factorized (when real), completed square.
Switch between Basic, Advanced, Methods, Applications.
Δ > 0 two real roots; Δ = 0 repeated root; Δ < 0 complex pair.
Turning point at x = −b/(2a). Minimizes if a > 0; maximizes if a < 0.
Vertex, factorized (when real), and completed square show structure.
Use our comprehensive quadratic equation solver to find roots, analyze parabolas, and explore mathematical properties. Get discriminant analysis, vertex form, factorization, completing the square steps, and real-world optimization applications. Perfect for students, engineers, and researchers working with quadratic functions, parabolic motion, and mathematical modeling.
Quadratic formula, factoring, completing the square with step-by-step solutions.
Vertex form, discriminant analysis, domain/range, concavity, and optimization insights.
Physics problems, engineering optimization, business modeling, and geometric applications.
Quadratic equation solver, quadratic formula calculator, discriminant analysis, vertex form converter, factoring quadratics, completing the square, parabola analysis, roots finder, quadratic function graphing, optimization problems, projectile motion calculator, maximum minimum finder, axis of symmetry, complex roots calculator, polynomial solver, algebraic equations, mathematical modeling.
Enhance your mathematical analysis with our complementary calculators. Try the Scientific Calculator for advanced computations, the Percentage Calculator for ratio analysis, or the Basic Calculator for fundamental arithmetic operations.
Important: This quadratic equation solver is designed as an educational and professional tool for mathematical analysis. While the calculator employs rigorous mathematical algorithms and provides accurate results, it is recommended that users independently verify critical calculations, especially for academic submissions, professional engineering applications, or commercial purposes. The tool provides multiple solution methods and comprehensive analysis to enhance understanding of quadratic functions and their real-world applications. Results should be interpreted within the context of the specific problem being solved.