Which of the following function definitions describes a quadratic variation?

Question

A. #f(x) = (x-1)^2#

B. #f(x) = x^2+1#

C. #f(x) = 3x^2#

D. #f(x) = 3x#

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Answer 1 · 2017-04-09T21:06:17

The third option, where #f(x) = 3x^2#

Using the radio button labels and ignoring the "Option..." labels, we have:

A. #" "f(x) = (x-1)^2 = x^2-2x+1#

B. #" "f(x) = x^2+1#

C. #" "f(x) = 3x^2#

D. #" "f(x) = 3x#

So all of A., B. and C. are described by quadratic functions, but only C. is directly proportional to the square of the parameter.

As I understand it, this means that only C. qualifies as a "quadratic variation".