Quadratic Solver

Un'equazione di secondo grado (o quadratica) ha la forma ax² + bx + c = 0, dove a≠0. Si chiama di secondo grado perché il grado massimo della variabile x è 2. Si risolve con la formula: x = (-b ± √(b²-4ac)) / 2a.

Il discriminante Δ = b²-4ac determina il tipo di soluzione: se Δ > 0 ci sono due soluzioni reali distinte, se Δ = 0 una soluzione reale doppia, se Δ < 0 due soluzioni complesse coniugate (nessuna soluzione reale).

La parabola y = ax² + bx + c ha il vertice nel punto di minimo (se a>0) o massimo (se a<0). Le coordinate del vertice sono: V = (-b/2a, -(b²-4ac)/4a). Il vertice è l'asse di simmetria della parabola.

A second-degree equation (quadratic) has the form ax² + bx + c = 0, where a≠0. It is called second-degree because the maximum degree of variable x is 2. It is solved with the formula: x = (-b ± √(b²-4ac)) / 2a.

The discriminant Δ = b²-4ac determines the type of solution: if Δ > 0 there are two distinct real solutions, if Δ = 0 one repeated real solution, if Δ < 0 two complex conjugate solutions (no real solutions).

The parabola y = ax² + bx + c has its vertex at the minimum point (if a>0) or maximum (if a<0). The vertex coordinates are: V = (-b/2a, -(b²-4ac)/4a). The vertex is the axis of symmetry of the parabola.

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