Answer
$-3$
Work Step by Step
The minimum value of $f(x)$ is the $y$-coordinate of the lowest point on the graph, which is at the vertex.\\
The $y$-coordinate of the vertex is $3$ therefore the minimum value of $f(x)$ is $3$.
The $x$-coordinate of the vertex is $-3$ thus, the value of $x$ for which $f(x)$ is the smallest is $-3$.