# How to graph quadratic functions

A polynomial equation in which the highest power of the variable is 2 is called a quadratic function. We arrive at the following graph when we draw up a quadratic function such as *y* = *x*^{2}:

We can easily see that we are not dealing with a straight line but a parabola, thus it is referred to as a non-linear function. When one has a positive coefficient before *x ^{2}* we have a minimum value, and if we have a negative coefficient we have a maximum value instead. See the graph below where

*y*= -

*x*:

^{2}A rule of thumb reminds us that when we have a positive symbol before *x ^{2}* we get a happy expression on the graph

**:)**and a negative symbol renders a sad expression

**:(**.

We graph our quadratic function in the same way as we graph a linear function. First we make a table for our x- and y-values. From the x values we determine our y-values.

Last we graph our matching x- and y-values and draw our parabola.

**Video lesson**

Graph f(x)=(x-4)^{2}+1