write an equation of a parabola with the given vertex and focus
Vertex: (1, -4)
Focus: (1, -3)
The standard form equation of a parabola with vertex (h, k) and focus (h, k + p) is:
(x - h)^2 = 4p(y - k)
Substitute the values of the vertex and focus into the equation:
(x - 1)^2 = 4(-1)(y + 4)
(x - 1)^2 = -4(y + 4)
(x - 1)^2 = -4y - 16
Therefore, the equation of the parabola with vertex (1, -4) and focus (1, -3) is:
(x - 1)^2 = -4y - 16