SOLUTION: what is the vertex, focus, and equation of directrix (y+3)^2 = -4(x-2)

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Question 1152038: what is the vertex, focus, and equation of directrix
(y+3)^2 = -4(x-2)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
what is the vertex, focus, and equation of directrix

The standard form is %28x+-+h%29%5E2+=+4p+%28y+-+k%29, where the focus is (h,+k+%2B+p) and the directrix is y+=+k+-+p.
If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of %28y+-+k%29%5E2+=+4p+%28x+-+h%29, where the focus is (h+%2B+p,+k) and the directrix is+x+=+h+-+p
%28y%2B3%29%5E2+=+-4%28x-2%29......here you have an equation of rotated parabola in vertex form
so,
h=2, k=-3, 4p=-4=>p=-1
= >vertex is at (2,-3)
=> focus is at (h+%2B+p,+k) =(2+-1,+-3) = (1,-3)
=> equation of directrix is +x+=+h+-+p=>+x+=+2+-+%28-1%29=>+x+=+2%2B1=>+x+=+3