Editing Order of approximation (section)

===Second-order===
''Second-order approximation'' is the term scientists use for a decent-quality answer. Few simplifying assumptions are made, and when a number is needed, an answer with two or more significant figures ("the town has {{val|3.9|e=3}}, or ''thirty-nine hundred'', residents") is generally given. As in the examples above, the term "2nd order" refers to the number of exact numerals given for the imprecise quantity. In this case, "3" and "9" are given as the two successive levels of precision, instead of simply the "4" from the first order, or "a few" from the zeroth order found in the examples above.

A second-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a [[quadratic polynomial]], geometrically, a [[parabola]]: a polynomial of degree&nbsp;2. For example:

: <math>x = [0.00, 1.00, 2.00],</math>
: <math>y = [3.00, 3.00, 5.00],</math>
: <math>y \sim f(x) = x^2 - x + 3</math>

is an approximate fit to the data. In this case, with only three data points, a parabola is an exact fit based on the data provided. However, the data points for most of the interval are not available, which advises caution (see "zeroth order").