**A quadratic function is a type of function that is characterized by being a second degree polynomial.**

In other words, a quadratic function is a function in which one of the elements has a small 2 as the upper index.

A quadratic function is also called a second degree function.

## Quadratic function formula

The functions are the representative form of the equations. So a quadratic function will be the same as a quadratic equation. So that:

As you can see, both expressions are the same, the only thing that the first is more oriented to be drawn and, the second, is used more in calculation.

## Properties of the quadratic function

The quadratic function will always be comprised in the first and fourth quadrants of a graph. This is because for any value of X introduced to the function, it will always return a positive value.

The quadratic function forms a symmetric parabola with the vertical axis.

The sign of the element containing the degree indicates whether it is a convex or concave function.

- If the sign is
**positive**-> the function will have a**minimum**in the X, and therefore, it will be**concave**. - If the sign is
**negative**-> the function will have a**maximum**in the X, and therefore it will be**convex**.

## Graphic

We can also think that if the function is positive it indicates that it is happy, then if we draw two eyes on top of the graph we can identify it as concave. On the contrary, if the function is negative, that is, it is sad, we will see that if we draw two eyes on the graph above, we can easily identify it:

This makes it easier to identify the function, right?

If we add or subtract any number to it, the function moves up or down, depending on the sign:

If we multiply the function by any number greater than 1, the width of the parabola becomes smaller:

If we divide the function by any number greater than 1, the width of the parabola becomes larger:

## Resolution method

The method used to solve quadratic functions is the following:

Surely this formula is familiar to you since it is widely used and appears frequently. Well, this formula is used to solve quadratic equations that comply with the following structure:

## Quadratic function example

Identify if the following function is a quadratic function:

The function a) is a function of degree 3, therefore, it is not a quadratic function. Also, because we can see that it does not form a parabola with the vertical axis.