Answer
vertex: $(5, 0)$
Parent function transfomations:
$5$ units to the right and reflection about the $x$-axis
Work Step by Step
RECALL:
The graph of the function $y=-a\cdot |x-h|+k$ has its vertex at $(h, k)$ and involves the following transformations of the parent function $f(x)=|x|$:
(1) a horizontal shift ($h$ units to the right when $h\gt0$, $|h|$ units to the left when $h\lt0$);
(2) a vertical shift ($k$ units up when $k\gt0$, $|k|$ units down when $k\lt0$);
(3) a vertical stretch (when $a \gt 0$) or vertical compression (when $0\lt a \lt 1$); and
(4) a reflection about the $x$-axis.
The given function can be written as:
$$y=-1\cdot |x-5|+0$$
The function has:
$a=1$, $h=5$, and $k=0$
Thus, its graph has its vertex at $(5, 0)$ and involves the following transformations of the parent function $f(x)=|x|$:
(1) $5$ units shift to the right; and
(2) a reflection about the $x$-axis
