解f(x)=sin^2x+2sinxcosx+3cos^2x,
=sin^2x+cos^2x+2sinxcosx+2cos^2x
=1+sin2x+2cos^2x
=2+sin2x+2cos^2x-1
=sin2x+cos2x+2
=√2sin（2x+π/4)+2
函數(shù)的對稱軸滿足2x+π/4=kπ+π/2,k屬于Z.
故函數(shù)的對稱軸為x=kπ/2+π/8,k屬于Z.
函數(shù)圖像的對稱中心滿足2x+π/4=kπ,k屬于Z
故函數(shù)圖像的對稱中心滿足x=kπ/2-π/8,k屬于Z,
故函數(shù)的對稱中心為（kπ/2-π/8,0）,k屬于A.