Answer:
The focus of a parabola is (0, -2), and the directrix is the line y = 0. Given this information, we can find the equation of the parabola in vertex form.
The vertex form of the equation for a parabola with its vertex at the point (h, k) and the focus at (h, k + p) or (h, k - p) is:
(y - k)² = 4p(x - h)
In this case, the vertex is (h, k) = (0, -1), and the focus is (h, k + p) = (0, -2). So, p = -1.
Now, we can plug these values into the vertex form equation:
(y - (-1))² = 4(-1)(x - 0)
Simplify:
(y + 1)² = -4x
So, the equation of the parabola in vertex form is:
y = (x²) - 1