Math Solvers/Algebra & Calculus/quadratic-polynomial

Quadratic Equation & Parabola Vertex Solver

Solve any quadratic polynomial ax² + bx + c = 0 with comprehensive KaTeX steps, discriminant analysis, vertex coordinate determination, and parabolic properties.

Polynomial Coefficients

Current Equation

Quadratic Coefficient (a ≠ 0)

Linear Coefficient (b)

Constant Term (c)

First Root (x₁)

3.0000

Real intersection root

Second Root (x₂)

2.0000

Secondary root

Discriminant (Δ)

1.0000

2 Real Roots (Δ > 0)

Parabola Vertex (h, k)

(2.500, -0.250)

Axis of symmetry: x = 2.500

KaTeX Step-by-Step Derivation

1. Quadratic Equation Form & Coefficients

Identified coefficients: a = 1, b = -5, c = 6.

2. Discriminant Evaluation (Δ)

Δ > 0: The equation has two distinct real roots.

3. Quadratic Formula Solution

Calculated roots: x_1 = 3.0000, x_2 = 2.0000.

4. Parabola Vertex & Geometry

The axis of symmetry is x = 2.5000. Parabola opens upwards (minimum point).

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Mathematical Formulation

Standard analytical and numerical formulations derived from classical algebra, linear algebra, and calculus principles.