The answer is ‘Parabola’...now, what’s the question?

Just how many questions can you ask to which the answer is “It’s a parabola!”? Douglas Butler suggests a few. Follow the links and you may be surprised. Alternatively you could pose some other questions that give wider access to the parabola.

I was taking a lesson recently with some 13 year-olds at in international school, for whom the words ‘parabola’ and ‘quadratic equation’ were not too well established, and I found myself asking as many questions as I could think of, to which the answer was ‘parabola’. The trouble is that, after a while, they gave that answer to all questions, including ‘What’s for lunch today?’!

Well here are some of the ideas I came up with, but this is list one that I am quite sure many readers will want to add to on the MTi forum. Just click away and explore! I have used JING (*) to record many of these using Autograph, but you should be able to do the same or similar steps in other graphing software that can import images, eg GSP, Cabri or Geogebra.

Please note the lack of reference to structures here - many may look parabolic in shape, but the likes of Sydney Harbour Bridge, the Wembley Arch, the St Louis Arch are usually inverted or upright catenaries. See the very good Wikipedia article on this subject (scroll past the mathematics!). This goes on to suggest that most suspension bridges are catenaries before the deck is attached, but then become parabolic in their final configuration! Worth investigating I would say - plenty of bridge images available, of course, via Google’s image search.