We know g(x) = 2(x-m)^2 + 3 and g(0) = 11

g(x) = 2(x-m)^2 + 3 , g(0) = 11

11= 2(0-m)^2 + 3
11-3 = 2(-m)^2
8 = 2m^2
8/2 = m^2
4 = m^2 or m^2 = 4
m = -2 or +2 (this is answer)