f-g=e(x-a)^2
f'-g'=2e(x-a)=0 at a
f-g=0 at a
f-g=e(x-a)^2+bx+c
f'-g'=2e(x-a)+b=b at a but 0 if b=0
f-g=e(x-a)^2+c=c at a