Final answer:
Changing the function from y = x^2 + 4 to y = x^2 + 1 results in the graph shifting 3 units down, with no other changes to the shape or orientation of the graph.
Step-by-step explanation:
The student's question pertains to how the graph of a quadratic function y = x^2 + 4 would change if the function was modified to y = x^2 + 1.
To understand this, one must recognize that these equations represent parabolas that open upwards, and the constant term represents the y-intercept of the graph. The original function has a y-intercept of 4, whereas the modified function has a y-intercept of 1. When comparing the two, the only change is in this constant term, which results in a vertical shift of the graph.
The graph of y = x^2 + 4 will shift downward by 3 units to become y = x^2 + 1. This is because the constant term has decreased by 3 units. This shift is purely vertical, with no horizontal movement, and it does not affect the shape of the parabola or its opening direction. So the correct answer is that the graph would shift 3 units down, which corresponds to option B.