Answer:
- x -4 = (-3/2)(y +1)^2
- vertex: (4, -1)
- focus: (3 5/6, -1)
- directrix: x = 4 1/6
Step-by-step explanation:
To get your desired form, you must divide the equation by -2. Then you have ...
x -4 = (-3/2)(y +1)^2
This form shows you the vertex is (h, k) = (4, -1).
When the scale factor "a" is written as 1/(4p), then the value of p is the distance from the focus to the vertex. We can find p from ...
(-3/2) = 1/(4p)
p = 1/(4(-3/2)) = -1/6
Since the parabola opens to the left, the focus is ...
(4-1/6, -1) = (3 5/6, -1)
and the directrix is in the opposite direction, at x = 4 1/6.
