Answer
(H) $y=-|x+2|$
Work Step by Step
RECALL:
The function $y=a \cdot f(x-h) + k$ involves the following transformations of the parent function $f(x)$:
The graph looks like an inverted V, so its parent function is $y=|x|$.
The graph of the parent function is shaped like an upward V.
The given graph is an downward V, so it must involve a reflection about the x-axis of the parent function.
Thus, a tentative equation of the function is $y=-|x|$
The vertex of the given function is a $(-2, 0)$.
This means that the graph involves a horizontal shift of $2$ units to the left of the parent function $f(x)$.
Thus, the tentative equation becomes $y=-|x+2|$.
Therefore, the equation of the given graph is $y=-|x+2|$.
