Question

2. A common situation that arises when we collect experimental data is that a simple curve can be fitted through a selection of data points when we only have a small data sample, but as we continue to collect further data, we can no longer fit the data exactly and must instead look for a curve of best fit. Consider, for instance, the equation y = 6 − 9x + 3x 2 and the data points (0, 6), (1, 0) and (2, 0). a) [1 mark] First confirm that the equation is able to exactly fit the three points. b) [1 mark] Suppose we now collect some additional data. If the data point (3, 4) is added to the above data, show that the equation above can no longer exactly fit all four data points. c) [4 marks] Using the quadratic formula from Question 1(a) above, find the parabola of best fit for the set of four data points.

Answer 1

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