Question

Consider the data points (–4, –14), (–2, –7), (0, –3),
(2, –2), and (6, –6). Which type of function would best model the data set?

Answer 1

A quadratic function (a parabola).

Reason: for the equally spaced x-values -4, -2, 0, 2 the y-values -14, -7, -3, -2 have first differences 7, 4, 1 and second differences 4−7 = −3 and 1−4 = −3 (constant). Constant second differences indicate a quadratic.