Quadratic function


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. Such that:

Function and equation

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.


Quadratic functions

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:

He drew

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:

Function scrolling

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

Function scrolling

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

Function scrolling

Resolution method

The method used to solve quadratic functions is the following:

Method of solving equations of the second degree

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:

Structure of quadratic equations

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.

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