Chapter 2 - Functions, Equations, and Graphs - 2-7 Absolute Value Functions and Graphs - Lesson Check - Page 111: 1

vertex: $(-4, -3)$ axis of symmetry: $x=-4$

RECALL: The function $y=a|x-h| + k$ has its vertex at $(h, k)$ and has the line $x=h$ as its graph's axis of symmetry. The given function can be written as: $$y=2|x-(-4)|+(3)$$ Thus, it has $h=-4$ and $k=-3$. Therefore, its vertex is $(-4, -3)$ and its graph's axis of symmetry is the line $x=-4$.