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".