To graph the equation $y = -2|x - 3| + 5$, you should follow these steps:

1. Understand the structure of the equation:

   • $y = |x - 3|$ represents the basic absolute value function, which is a V-shaped graph with the vertex at $(3, 0)$.
   • The factor of $-2$ reflects and stretches the graph vertically by a factor of 2, making the V open downward and steeper.
   • The $+5$ at the end shifts the entire graph up by 5 units.

2. Determine the vertex: The vertex of the graph is at $(3, 5)$, because the equation is of the form $y = -2|x - 3| + 5$.

3. Plot key points:

   • For $x = 3$, $y = 5$, so plot the point $(3, 5)$.
   • For $x = 4$, calculate $y = -2|4 - 3| + 5 = -2(1) + 5 = 3$, so plot $(4, 3)$.
   • For $x = 2$, calculate $y = -2|2 - 3| + 5 = -2(1) + 5 = 3$, so plot $(2, 3)$.
   • As $x$ moves further away from 3, the absolute value term increases, and the graph continues downward with a slope of $-2$ to the left and right of the vertex.

4. Sketch the V-shape: The graph should form a V with the vertex at $(3, 5)$, opening downwards and stretching steeper due to the factor of $-2$.

If you'd like, I can help you visualize this graph with the draggable points. Would you like me to generate a graph for you?