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, in the first place, derives from Latin, exactly from “functio”, which is the result of the sum of two well differentiated parts: the verb form “functus”, which means “to fulfill”, and the suffix “-tio”, which is used to indicate “action and effect.”

-Quadratic, secondly, we can state that it means “relative to the square” and that it also derives from Latin. It is exactly the result of the sum of three lexical components of that 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 **math** it is called **function** the link between two sets through which each element of the first set is assigned only one element of the second set or none at all. The idea of **quadratic**, on the other hand, it is also used in the field of mathematics, alluding to what is related to the **square** (the product of multiplying a quantity by itself).

In this framework, it is called **quadratic function** to the mathematical function that can be expressed as a **equation** which has the following form: **f (x) = ax squared + bx + c**.

In this case, **to**, **b** Y **c** are the terms of the equation: **real numbers**, with **to** always with a different value than **0**. At the end **ax** squared is the quadratic term, while **bx** is the linear term and **c**, the independent term.

When all the **terms**, there is talk of a **complete quadratic equation**. On the other hand, if the linear term or the independent term is missing, it is a **incomplete quadratic equation**.

## Graphic representation

The graphical representation of a quadratic function is a **parable**. The orientation of the parabola, the vertex, the axis of symmetry, the intersection point with the coordinate axis and the intersection point with the abscissa axis are characteristics that vary according to the **values** of the quadratic equation in question.

In addition to all the above, we have to point out that this parable may be of two types: convex parable or concave parable. 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 a **geometry** and in kinematics, among other contexts, expressed through different equations.