Quadratic Equation Solver

A quadratic equation is any equation in the form ax² + bx + c = 0, where a is not zero. These appear across mathematics, physics, engineering, economics, and computer science. The solver finds the roots (solutions) of any quadratic equation and shows the complete working, including the graph of the parabola. Entering coefficients: Enter the values of a, b, and c from your equation. For example, for 2x² − 5x + 3 = 0, enter a = 2, b = −5, c = 3. Fractional and decimal coefficients are supported. Click Solve. What the solver shows: Discriminant (b² − 4ac) — determines the nature of the roots before calculating them: Positive: two distinct real roots Zero: one repeated real root (the parabola touches the x-axis at one point) Negative: two complex (imaginary) conjugate roots (the parabola does not cross the x-axis) Roots (x₁ and x₂) — calculated using the quadratic formula: x = (−b ± √discriminant) / 2a. Exact simplified forms shown where possible, decimal approximations always included. Vertex — the turning point of the parabola. x-coordinate = −b / 2a; y-coordinate = f(x-vertex). Axis of symmetry — the vertical line x = −b / 2a that the parabola is symmetric around. Graph — a plot of the parabola showing the x-axis intercepts (if they exist), vertex, and axis of symmetry. Step-by-step working: Each step of the quadratic formula application is shown — substitution, discriminant calculation, square root, and final root calculation. Useful for homework, exam preparation, and understanding the process. Common applications: projectile motion (height as a function of time), optimizing revenue and profit functions, finding intersection points, and solving geometric problems involving areas.