How to find the equation of a quadratic function from its graph :: squareCircleZ

Murray Bourne of squareCircleZ has posted on 'How to find the equation of a quadratic function from its graph'. This is indeed the type of discussion and exercise that we need to see more of.  Not only does it promote a deeper understanding of the mathematics than the reverse but it is also relevant to more practical applications. Occasionally we do come up with a formula and want to see what it looks like but, especially when it comes to specific examples as opposed to general patterns, it is more often that we have data and want to find or verify a formula.  One of the activities in my own “Blue Meanies” game (at http://qpr.ca/math/applets/meanies/ )asks students to “guess” the equation of a parabola through three points by imagining the curve and using its geometry (in various ways) to determine the equation. Of course in such "modelling" problems, with limited data there will be many possible model types that can be used, and there is an interesting interplay between fitting with a particular class of functions (eg polynomial or exponential) and giving reasons why one or other such class might be more appropriate in a given situation.

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