The equation of the parabola is x² = -12 (y - 1)
How to find the equation
To determine the equation of the parabola, we can use the standard form for a downward-opening parabola:
(x - h)² = 4p(y - k)
where (h, k) is the vertex of the parabola and
p is the distance between the vertex and the focus
Given that the vertex is at (h, k) = (0, 1) and the parabola intercepts the x-axis at (-3.5, 0) and (3.5, 0).
Focus (0, -2)
p = |-2 - 1| = 3
substitute these values into the standard form:
(x - 0)² = 4 (3) (y - 1)
x² = -12 (y - 1)