Chapter 11 - Quadratic Functions and Equations - 11.6 Quadratic Functions and Their Graphs - 11.6 Exercise Set - Page 741: 50

The vertex is $(-4,-12)$ The axis of symmetry is $x=-4.$ The maximum function value is $-12.$

$f(x)=-\displaystyle \frac{1}{4}(x+4)^{2}-12$ $a=-\displaystyle \frac{1}{4}$ $h=-4$ $k=-12$ The vertex is $(h, k)$, and the axis of symmetry is $x=h.$ For $a\gt 0$, the minimum function value is $k$. For $a\lt 0$, the maximum function value is $k.$ --- The vertex is $(-4,-12)$ The axis of symmetry is $x=-4.$ Since $a\lt 0$, the maximum function value is $-12.$