Update – note that all the Desmos posts now have their own page.
This is easy to use and the ability to set up a page then save the url means teachers can set up pages for students to explore families of graphs.
(See Explore Graphs.)
Variables can easily be changed to see the effect on the graph, for example click on a, b or c to change the value of the variable and note the change in the parabola.
There are several examples already set up, for example one could choose the vertex form for a parabola from the examples list.
Wondering if what we see now will remain free I sent this enquiry to Desmos who replied very swiftly and courteously that it would indeed (and more to come!)
This YouTube video provides an introduction to the calculator.
For other graph plotters online see the resources here.