Question

determine the graph of the absolute value function that opens downward and has a vertex at (-3, 6). choose the correct answer from each drop - down menu to complete the statement. the graph of the function has a choose the correct answer value of choose the correct answer. the drop - down options include maximum and minimum.

Explanation:

Step1: Recall absolute value function properties

The general form of an absolute value function is \( y = a|x - h| + k \), where \((h, k)\) is the vertex. If \( a < 0 \), the graph opens downward. For a graph opening downward, the vertex represents the maximum point (since the graph opens down, the vertex is the highest point, so it has a maximum value).

Step2: Determine the type of extremum

Given the function opens downward and has a vertex at \((-3, 6)\), the vertex is the highest point on the graph. So the graph has a maximum value (at the vertex's \( y \)-coordinate, which is 6 here).

Answer:

maximum