Question

question 1-13
which of the following models the absolute value function $y = -2|x + 3| - 6$

Explanation:

Step1: Identify vertex of the function

The vertex form of an absolute value function is $y = a|x - h| + k$, where $(h,k)$ is the vertex. Rewrite the given function: $y = -2|x - (-3)| - 4$. So the vertex is $(-3, -4)$.

Step2: Determine opening direction

Since $a = -2 < 0$, the graph opens downward (points downward like an inverted V).

Step3: Match with options

Look for the graph with vertex at $(-3, -4)$ that opens downward. The first graph (topmost option) has this vertex and opens downward.

Answer:

The topmost graph (first option, the inverted V with vertex at (-3, -4))