Final answer:
The equation of a parabola with focus (0, 5) and directrix y = -1 is y = 1/12 x², which represents a vertical parabola opening upwards.
Step-by-step explanation:
The equation of a parabola can be found using the definition that a parabola is the set of all points equidistant from the focus and the directrix. For a parabola with focus (0, 5) and directrix y = -1, the vertex is halfway between the directrix and the focus, so the vertex is at (0, 2). The distance from the vertex to the focus and directrix is 3, which is the value of 'p' in the parabola equation (4p)y = (x - h)², where (h, k) is the vertex.
Therefore, the equation for this parabola is y = 1/12 x². This equation indicates a vertical parabola that opens upwards because the coefficient of x² is positive.