To discober which quadratic curve best fit this set of data, all we need to do is replace x from every equation with the coordinate x from every data. The curve that best fit this set is the one that best approaches to y coordinate.
Trying to do this with the equation C. (0.13x^2-0.04*x+17.5), we got the best aproximation to y coordinate using the x coordinate.
For example, with the data (-16,51.4), we replace x by -16 and get: 0.13*(-16)^2-0.04*(-16)+17.5 = 51.42
For data (-12,38) we get: (-12)^2-0.04*(-12)+17.5 = 36.7
For data (-8,25) we get: 26.14.
And by doing this with all set of data, we conclude that equation C. is the one that best fit this set.