Chapter 8 - Graphing Quadratic Functions - 8.4 - Graphing f(x) = a(x-h)^2 + k - Exercises - Page 447: 37

Graph $D$

The function in the form $y=a(x-h)^2+k$ has a vertex at $(h,k)$. Given: $$y=\frac13(x-1)^2+3.$$ It follows that $a=\frac{1}{3}$, $h=1$, $k=3$. The vertex is $$(h,k)=(1,3)$$ and the parabola opens up since $a>0$. The graph which fits is graph $D$.