Answer:
A. f(x) = -4|x +2| +3
Explanation:
You want the function that matches the graph of the absolute value function shown. Its vertex is (-2, 3) and it opens downward.
Opens downward
The parent function must be reflected across the x-axis for its graph to open downward. That means the function must be multiplied by a negative number. (Eliminates choices B and D.)
Translated upward
The vertex of the function is translated up 3 units, so 3 will be added to the function value. (Eliminates choices C and D.)
The only remaining viable choice is A.
A. f(x) = -4|x +2| +3
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Additional comment
The translation left 2 units replaces x in the function by (x -(-2)) = (x+2). This matches choice A and eliminates choice C.
g(x) = a·f(x -h) +k
translates f(x) by (h, k). When a < 0, reflects f(x) across the x-axis. Here, (h, k) = (-2, 3).