When drawing a graph such as #f(x)# you pretty much only need to find the points for where #f(x)=0# and the maxima and minima and then draw the lines between these.

For example, you could solve #f(x)=0# by using the quadratic equation. To find the maxima and minima you can dervivate the function and find #f'(x)=0#.

#f(x)=x^2+1# does not have any points for where the function is zero. But it has a minimal point located at #(0,1)# which can be found through #f'(x)=0#.

Since it's harder to know how the graph is illustrated without the points where #f(x)=0#, and without maxima and minima we can add a table for the graph. Which we can do with a set of random #x# values. In order to see the #f(x)# values at the #x# values.

You can view a method for this here.