Today I posed a fairly common type of 'quadratic functions' question to my first year Maths HL students. The question is also suitable for SL students although questions like this are less common on SL exams. It is a 'fair' question for both HL and SL students. The reason I'm highlighting it in a blog post came about because the way in which I and some of my students verified our answer to it brings up some interesting questions about how technology might blur the distinction between verification (checking answer) and proof (formal, analytic process of obtaining answer).

The ensuing brief discussion in class was an opportunity to ask an interesting question about knowledge. Are results (knowledge) obtained by means of technology any more or less reliable than that obtained without the use of technology?

OK, below is the question and its solution. But, like I said, what generated an interesting discussion was how some of us decided to use the dynamic features of our TI-Nspire CX handheld device (not 'calculator') to check the answer ... and whether this check could be considered a legitimate way to solve/prove.

Below is a short video of what we did on a TI-Nspire CX to check the answer.  If we skipped the analytic solution (shown above) and obtained the answer from the animated graph shown below, would that be considered a legitimate solution?