Final answer:
The graph of y = 2 + (x - 3)^2 is increasing over the interval (3, infinity) because it represents an upward-opening parabola with its vertex at point (3, 2).
Step-by-step explanation:
The graph of the function y = 2 + (x - 3)^2 represents a parabola that opens upward since the coefficient of the quadratic term is positive. The vertex of this parabola is at the point (3, 2). To determine over what interval the graph of the parabola is increasing, we look at the behavior of the function to the right of the vertex. Since the parabola opens upward, it is decreasing to the left of the vertex and increasing to the right. Therefore, the graph is increasing over the interval (3, infinity). Hence, the correct answer to the question 'Over what interval is the graph of y = 2 + (x - 3)^2 increasing?' is D. (3, infinity).