Algebra-1

1. Highest Point (Vertex): The highest point (vertex) of the graph is at (-6, 0).

2. Symmetry: The function is symmetric about x = -6.

3. Opening Direction: The graph opens downward.

Let’s analyze the options:
A. g(x) = -|x + 6|:
This function is symmetric about x = -6 and opens downward. Its vertex is at (-6, 0), which matches the description.

B. g(x) = |x - 6|:

This function is symmetric about x = 6 and opens upward, so it does not match the symmetry or the opening direction.

C. g(x) = -|x| + 6:...