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## All parabolas are symmetrical, right?

Today I was teaching one of my classes about drawing graphs. It was going well, we’d moved from linear to quadratic and discussed the shape. After a few minutes of plotting quadratic graphs from equations one of the students asked, “Sir, these parabolas are all symmetrical, right?” we discussed it briefly and he decided that yes they were. Then he carried on working. I was circulating the class and I noticed he was flying through the work so I asked him to explain why he was going so much faster. He said, “I’ve found a short cut sir, cos they’re symmetrical you once you see when they start repeating you can easily just work out the points from the ones you know.” I was impressed by his mathematical thinking, although I wasn’t as impressed with his explanation, although he did manage to refine it and explained it much better to one of his class mates who had overheard our discussion and wanted further explanation.