The parent function for an absolute value function is:
If a is positive, the graph will open upward, and if a is negative, it will open downward. Given that the graph opens downward, we know a must be negative.
Next, h represents the horizontal shift of the graph. Given that the vertex is at (-2,k), we know that h = 2.
The k value does not matter because in the given characteristics we are given a general k value that will work with any graph.
Finally, we need to find which graph passes through (-3, -1). To meet the requirements discussed above, we can narrow the answer to C or D. Now just plug in -3 for x in both functions, and whichever one equals -1 at x=-3 is our answer:
C) -4|-3 + 2| + 3 = -4(1) + 3 = -1
D) -4|-3 + 2| - 3 = -4(1) - 3 = -7
The answer is C.
