Final answer:
The equation for the absolute value function with a vertex at (2,3) and x-intercepts at (-1,0) and (5,0) is 0 = |x-2| + 3.
Step-by-step explanation:
The correct equation for the absolute value function with a vertex of (2,3) that crosses the x-axis at (-1,0) and (5,0) is 0 = |x-2| + 3. The absolute value function is of the form y = a|x-h| + k, where (h,k) is the vertex. The graph of the function will be a V-shaped curve that has its vertex at the point (2,3). Since the x-intercepts are (-1,0) and (5,0), this implies that the function is equidistant from these points to the vertex. Therefore, the function will increase and decrease at the same rate from the vertex, so the stretch factor 'a' is assumed to be 1. The correct answer corresponds to option 'b' in the provided choices.