Neliökäyrä

Neliökäyrä is a Finnish term that translates to "quadratic curve" or "parabola" in English. It refers to a curve that is the graph of a quadratic function. A quadratic function is a polynomial function of degree two, meaning it has the general form y = ax^2 + bx + c, where a, b, and c are constants, and a is not equal to zero.

The characteristic shape of a neliökäyrä is a parabola. This shape is symmetrical, with a single turning point called the vertex. Depending on the sign of the coefficient 'a', the parabola will either open upwards (if a > 0) or downwards (if a < 0). The roots of the quadratic equation, which are the x-values where the curve intersects the x-axis, can be found using the quadratic formula or by factoring.

Neliökäyrät have numerous applications in various fields. In physics, they describe the trajectory of projectiles under the influence of gravity. In engineering, they are used in the design of satellite dishes and reflectors due to their ability to focus or disperse parallel rays. In economics, they can model cost or profit functions. The study of neliökäyrät is a fundamental topic in algebra and geometry.