## Algebra 2 Common Core

vertex: $(-6, 0)$ $6$ units shift ot the left and a vertical stretch by a factor of $3.$
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 $k\lt0$); and (3) a vertical stretch (when $a \gt 0$) or vertical compression (when $0\lt a \lt 1$), The given function can be written as: $$y=3|x-(-6)|+0$$ The function has: $a=3$, $h=-6$, and $k=0$ Thus, its graph has its vertex at $(-6, 0)$ and involves the following transformations of the parent function $f(x)=|x|$: (1) $6$ units shift to the left; and (2) a vertical stretch by a factor of $3$