The vertex of the graph of $$ f(x)=-\frac{1}{2}|x+3|+1 $$ is Choose... The graph opens Choose

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The function is given by 
$$
f(x)=-\frac{1}{2}|x+3|+1.
$$

1. To find the vertex, note that the absolute value function $$ |x+3| $$ reaches its minimum value (i.e., 0) when
   $$
   x+3 = 0 \quad \Rightarrow \quad x = -3.
   $$
2. Substitute $$ x=-3 $$ into the function:
   $$
   f(-3)=-\frac{1}{2}\cdot|(-3)+3|+1 = -\frac{1}{2}\cdot0+1 = 1.
   $$
   Hence, the vertex is $$\boxed{(-3,\,1)}$$.

3. The coefficient of the absolute value term is $$-\frac{1}{2}$$, which is negative. This indicates that the graph opens downward.

Thus:

- The vertex of the graph is $$\boxed{(-3,\,1)}$$.
- The graph opens $$\boxed{\text{downward}}$$.
The vertex of the graph is at (-3, 1) and the graph opens downward.

The vertex of the graph of is Choose… The graph opens Choose

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