Population of scores has μ = 50 and σ = 12. if you subtract five points from every score in the population, then the new standard deviation will be

The mean of the sample is 50 and the standard deviation is 12. If 5 is subtracted from each of the values the standard deviation will remain the same, as the standard deviation is the distance of each value from the mean. Since all the scores are subtracted by 5, the effective distance from the mean is going to be the same but the mean will be reduced by 5.

Every y value is 2 more in f(x) so we have 

f(x) = x^2 + 2