What is the equation of a parabola if the vertex is (1, 4) and the directrix is located at
y = 7?
A.y = 12(x – 4)^2 – 1
B.y = -12(x + 4)^2 + 1
C.y = -1/12(x – 1)^2 + 4
D.y = 1/12(x + 1)^2 – 4
the parabola x^2 = 4py has
vertex at (0,0)
focus at (0,p)
directrix at y = -p
since y=7 is located 3 units above the vertex, p = -3
and so the translated parabola is
(x-1)^2 = -12(y-4)
or,
y = -1/12 (x-1)^2 + 4