Before entering fully into the meaning of the term quadratic function, it is necessary, first, to discover the etymological origin of the two words that shape it:
-Function, in the first place, derives from Latin, exactly from "functio", which is the result of the sum of two distinct parts: the verbal form "functus", which means "to fulfill", and the suffix "-tio", which is used to indicate "action and effect".
-Second, in the second place, 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 it has received the action", and the suffix "-tico", which means "relative to".
In the field of mathematics it's called function the link between two sets through which each element of the first set is assigned a single element of the second set or none. The idea of quadratic On the other hand, it is also used in the field of mathematics, referring to what is related to square (the product of the multiplication of 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 and 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 are present 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 .
The graphical representation of a quadratic function is a parable . The orientation of the parabola, the vertex, the axis of symmetry, the cut-off point with the axis of the coordinates and the cut-off point with the axis of the abscissa are characteristics that vary according to the values of the quadratic equation in question.
In addition to all of the above, we have to point out that this parable can be of two types: convex parable or concave parabola. The first is the one that is identified because its arms or branches are oriented downwards and the second is characterized in that those arms or branches are oriented upwards.
In this sense, it should be stressed that the parabola will be concave when a> 0 (positive). On the contrary, it will be convex when a <0 (negative). In the same way, it is interesting to know that the solutions or roots of the quadratic function are fundamental because they make known the intersection points of the parabola with respect to the axis of abscissa. It should be noted that quadratic functions appear in the geometry and in kinematics, among other contexts, expressed by different equations.