The correct answer is $-7$ . For a quadratic function defined by an equation of the form $f(x) = a(x - h)^2 + k$, where $a$, $h$, and $k$ are constants and $a > 0$, the function reaches its minimum when $x = h$. In the given function, $a = 1$, $h = -7$, and $k = 4$. Therefore, the value of $x$ for which $f(x)$ reaches its minimum is $-7$.