Final answer:
The graph of g(x) = 3x^2 + 6 is a steeper and upwardly shifted parabola compared to the graph of f(x) = x^2, due to the larger coefficient and constant term.
Step-by-step explanation:
To compare the graph of g(x) = 3x2 + 6 with the graph of f(x) = x2, let's discuss how each term affects the overall shape and position of the parabola. Both equations represent parabolas since they are quadratic functions. The graph of f(x) is a standard parabola with its vertex at the origin (0,0) that opens upwards, since the coefficient of x2 is positive.
For the graph of g(x), the coefficient of x2 is 3, which means it will be steeper than f(x) since the coefficient is greater than 1. Moreover, there is a constant term +6, which causes the entire graph to shift upward by 6 units. Therefore, the vertex of g(x) will be higher on the y-axis compared to f(x). In summary, both graphs will have the same general shape being parabolas, but g(x) will be a narrower and higher parabola compared to f(x).