Chapter 8 - Graphing Quadratic Functions - 8.4 - Graphing f(x) = a(x-h)^2 + k - Exercises - Page 447: 36

Graph $A$

The function in the form $y=a(x-h)^2+k$ has a vertex at $(h,k)$. Given: $$y=-\frac12(x-1)^2+3.$$ It follows that $a=-\frac{1}{2}$, $h=1$, $k=3$. The vertex is $$(h,k)=(1,3)$$ and the parabola opens down since $a<0$. The graph which fits is graph $A$.