kwadratowa

Kwadratowa is the feminine singular form of the Polish adjective kwadratowy, meaning square-shaped or quadratic. It is used with feminine nouns, such as funkcja (function), figura (figure), or liczba (number). The masculine form is kwadratowy and the neuter form kwadratowe. In everyday and mathematical usage, kwadratowa signals a relationship to a square or to quadratic mathematics.

In mathematics, kwadratowa appears in several standard terms. Równanie kwadratowe refers to a quadratic equation of the second degree in one variable, typically written as ax^2 + bx + c = 0 with a ≠ 0. Funkcja kwadratowa denotes a quadratic function, commonly written as f(x) = ax^2 + bx + c; its graph is a parabola. Liczba kwadratowa means a square number, i.e., a number that is the square of an integer. The discriminant, Δ = b^2 − 4ac, is used to determine the number and nature of the roots of a równanie kwadratowe. The graph of a kwadratowa funkcja has a characteristic U-shaped form and displays a vertex and an axis of symmetry.

Etymology and usage: kwadratowa derives from kwadrat, meaning square, with the adjectival suffix -owa to form feminine agreement. It is common in Polish mathematical and descriptive prose to pair the feminine form with feminine nouns, e.g., figura kwadratowa or liczba kwadratowa, and to refer to quadratic concepts through phrases like równanie kwadratowe or funkcja kwadratowa.