Question

The vertex of a parabola is at the point (3,1), and its focus is at (3,5). What function does the graph represent

Answer 1

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.