The kid responded by saying that he always learned it the opposite way: you start with the graph and from that you can deduce information about the maxima,minima, inflection points and intercepts etc. It never occurred to him that you could do it in the reverse manner. Bear in mind that this wasn't a dumb kid, but the material was presented differently because of the availability of the graphing calculator.

One of the side benefits of being able to do math in your mind or manually is that you can estimate what the answer is before using a computer or calculator. Then, if you make an all to common entry error and get an incorrect result, you can detect it. Otherwise, you need to try entering the values at least twice to see if you get a different answer. Even that doesn't work if you make the same mistake. I've seen too many people just push some buttons and accept the result no matter how absurd because they didn't realize they made an entry error.