The concept of a quadratic function appears in the field of mathematics.
Before entering fully into the meaning of the term quadratic function, it is necessary, first of all, to discover the etymological origin of the two words that give it its shape:
-Function, first of all, derives from Latin, exactly from “functio”, which is the result of the sum of two very different parts: the verbal form “functus”, which means “to fulfill”, and the suffix “-tio”, which is used to indicate “action and effect.”
-Quadratic, secondly, we can explain that it means “relative to the square” and that it also derives from Latin. Exactly it is the result of the sum of three lexical components of said language: the word “quattuor”, which means “four”; the particle “-atos”, which is used to indicate “that has received the action”, and the suffix “-tico”, which means “relative to”.
What is a quadratic function
In the field of mathematics , the link between two sets is called a function through which each element of the first set is assigned a single element of the second set or none at all. The idea of quadratic , on the other hand, is also used in the field of mathematics, referring to that related to the square (the product of multiplying a quantity by itself).
In this framework, the mathematical function that can be expressed as an equation that has the following form is called a quadratic function : f (x) = ax squared + bx + c .
In this case, a , b and c are the terms of the equation: real numbers , with a always having a value different from 0 . Al term ax squared is the quadratic term, while bx is the linear term and c is the independent term.
When all the terms are present, we speak of a complete quadratic equation . On the other hand, if the linear term or the independent term is missing, it is an incomplete quadratic equation .
Understanding what a quadratic function is can be complicated.
The graphic representation
The graphical representation of a quadratic function is a parabola . The orientation of the parabola, the vertex, the symmetry axis, the point of intersection with the coordinate axis and the point of intersection with the abscissa axis are characteristics that vary according to the values of the quadratic equation in question. .
In addition to everything stated above, we have to point out that this parabola can be of two types: convex parabola or concave parabola. The first is the one that is identified because its arms or branches are oriented downwards and the second is characterized because those arms or branches are oriented upwards.
In this sense, it must be emphasized that the parabola will be concave when a > 0 (positive). On the contrary, it will be convex when in geometry and in kinematics, among other contexts, expressed through different equations.