f(x)=x^2+mx+3
f(x+2)为偶函数
f(x+2)=(x+2)^2+m(x+2)+3
=x^2+4x+4+mx+2m+3
=x^2+(4+m)x+2m+7
x^2+(4+m)x+2m+7为偶函数
x^2+(4+m)x+2m+7=(-x)^2+(4+m)(-x)+2m+7
4+m=0
m=-4