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

The vertex of the function \( f(x)=-\frac{1}{2}|x+3|+1 \) can be found by identifying the point where the value of the absolute function is minimized. In this case, the vertex occurs at \( x = -3 \) and \( f(-3) = 1 \), so the vertex is \((-3, 1)\). As for the opening direction, since the coefficient of the absolute value function is negative (\(-\frac{1}{2}\)), the graph opens downwards. Imagine a sad face instead of a happy one; it's frowning because it's losing height!