Considering the given focus and directrix, the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
The equation of a parabola, with a directrix in y, is:
[tex]y - k = a(x - h)^2[/tex]
In which:
In this problem, we have that the x-coordinate of the vertex is h = 0.
From the focus and the directrix, we have that:
k+C = -9.5
k - c = 9.5.
Hence k = 0, C = -9.5 = a = 0.25C = -2.375.
Thus the equation of the parabola is given by:
[tex]y = -2.375x^2[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/26144898
