Final answer:
The vertex of the parabola described by g(x)=(9/7)(x-3)²+1 is (3, 1), and since the parabola opens upwards, it has no maximum value; the vertex represents the minimum point.
Step-by-step explanation:
The equation g(x)=(9/7)(x-3)²+1 represents a parabola in vertex form. The vertex form of a parabola is written as f(x)=a(x-h)²+k, where (h, k) represents the vertex of the parabola. In this case, the equation can be compared to the vertex form, allowing us to identify the vertex as (3, 1).
Since the coefficient a=(9/7) is positive, the parabola opens upwards. This indicates that the value at the vertex is the minimum value of the parabola. Hence, there is no maximum value for this parabola, as the value of g(x) will increase without bound as x moves away from 3.