Final answer:
The vertex of the graph of f(x) = -3 |x-1| is the point (-1, -3).
Step-by-step explanation:
The vertex of the graph of f(x) = -3 |x-1| is the point (-1, -3).
The function f(x) = -3 |x-1| represents a V-shaped graph called an absolute value function. The vertex of this graph is the lowest point on the graph.
When the value inside the absolute value function is positive, the graph takes the same shape as the line without the absolute value. When the value inside the absolute value function is negative, the graph is reflected about the x-axis. In this case, since the value inside the absolute value function is (x-1), the vertex is located at (1, -3).