Final answer:
The function represented by the graph is f(x) = 16(x-3)^2 + 1.
Step-by-step explanation:
The equation of a parabola with a vertex at (h,k) and a focus at (h, k+p) can be written as:
(x-h)^2=4p(y-k)
In this case, the vertex of the parabola is (3,1) and the focus is (3,5). So, the equation of the parabola is:
(x-3)^2=4(5-1)(y-1)
Simplifying this equation, we get:
(x-3)^2=16(y-1)
Therefore, the function represented by the graph is f(x) = 16(x-3)^2 + 1.