Final answer:
The equation of the parabola is (x - 1)² = 4.5(y + 0.5).
Step-by-step explanation:
To find the equation of the parabola, we need to determine the vertex and the equation of the axis of symmetry. The vertex is the midpoint between the focus and the directrix. In this case, the vertex is at (1, -0.5) and the axis of symmetry is x = 1. The equation of the parabola can be written in the form (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus. Since the vertex is at (1, -0.5) and the focus is at (1, -3), p = |-0.5 - (-3)|/2 = 2.25/2 = 1.125.
Therefore, the equation of the parabola is (x - 1)² = 4(1.125)(y + 0.5), or (x - 1)² = 4.5(y + 0.5).