Let's use this to make a connection with the graph of Standard Parabola Guy:

                       a graph of a standard parabola  ...  eventually all x's will be involved in the graph as it becomes wider and wider

Notice that this parabola gets wider and wider...  Eventually, if we kept drawing, ALL x's would be involved in the graph.

                                             a graph of a standard parabola  ...  no part of the graph is below the x axis, meaning that all y values are positive

And notice that the y guys go from zero up.
This matches up with our function box thinking!

domain= ( -infinity, infinity)
range= [ 0 , infinity )