Kwadratische

In Dutch mathematics, kwadratisch is an adjective describing anything related to degree-two structures. It is commonly used with nouns such as kwadratische functie (quadratic function), kwadratische vergelijking (quadratic equation) and kwadratische vorm (quadratic form). A kwadratische uitdrukking, in English often called a quadratic expression, is a polynomial of degree two and is typically written in the standard form ax^2 + bx + c with a ≠ 0.

A kwadratische vergelijking can be solved by factoring, completing the square, or by the quadratic formula x = [-b ± sqrt(b^2 - 4ac)]/(2a). The discriminant Δ = b^2 - 4ac determines the number and type of real roots. The parabola corresponding to the quadratic function has its vertex at x = -b/(2a) and y = f(-b/(2a)).

As a graph, a kwadratische functie opens upward when a > 0 and downward when a < 0. It models many real-world phenomena, including projectile motion, optimization problems, and area measurements. The concept is closely connected to completing the square, a method that rewrites ax^2 + bx + c as a(x − h)^2 + k, with h = -b/(2a) and k = c − b^2/(4a).