I finally found a balance between graphing using technology and doing things the old fashioned way. Today in Algebra II, I added a couple small things to the assignment on filling out tables and then graphing the results for polynomial equations. I had the students write down the number of possible zeros, if it were an even or odd function and number of possible turns. The next step was using Free Graph calc to enter the equation so they could switch to the table. They copied the values down on the table but before I let them go to the graph. I showed them how to read the graph for zero's, max, min from the table. Final step was to look at the graph and compare the information we got off the table with the graph and they drew the graph from the iPad. We are going to do this again tomorrow and the next day to give them additional practice in understanding the correlation among the equation, the table, and the graph itself.
I think we can get by without always having students do it only on the calculator or only by hand. In the working world, they will be using graphing calculators or programs to do much of the work we do in class but they need to know how to interpret the information they are given. I know I tend to rush through explanations and I've had to make myself slow down and only give them one step at a time so they follow along without getting lost.