To find the equation of a parabola in vertex form, we use the formula y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. In this case, the vertex is given as (3, 2), so we substitute h = 3 and k = 2 into the formula, resulting in y = a(x-3)^2 + 2. To find the value of 'a', we use the point (13, 8) that the parabola passes through. By substituting x = 13 and y = 8 into the equation, we can solve for 'a'. After simplifying, we find that a = 3/50. Substituting this value back into the equation gives us the final equation of the parabola: y = (3/50)(x-3)^2 + 2.