Final answer:
Option B is the correct answer. When the value of 'h' in the parabolic equation 'y = a(x-h)^2 + k' is doubled, the vertex of the parabola shifts horizontally, moving to a point that is twice as far from the y-axis.
Step-by-step explanation:
The graph of the equation y = a(x-h)^2 + k represents a parabola with the vertex at point (h, k). The graph's vertex is the highest or lowest point on the parabola, depending on whether the parabola opens upwards or downwards, which is determined by the sign of a. If the value of h is doubled, as in changing from h to 2h, the vertex of the parabola moves horizontally along the x-axis to (2h, k). This means the vertex has moved to a new position that is twice as far from the y-axis. Therefore, the correct answer to how the graph changes when the value of h is doubled is:
B: The vertex of the graph moves to a point twice as far from the y-axis.