Final answer:
The equation of the parabola is x^2 = 6(y - 5).
Step-by-step explanation:
The equation of a parabola with vertex (h, k) and focus (h + p, k) is given by the equation (x - h)^2 = 4p(y - k), where (h, k) represents the vertex and p represents the distance between the vertex and the focus. In this case, the vertex is (0, 5) and the focus is (3/2, 5), so the equation of the parabola is (x - 0)^2 = 4(3/2)(y - 5), which simplifies to x^2 = 6(y - 5).