Question 1198581: Identify the vertex, focus, and directrix for (y+3)^2=4(x-3).
One of the following is the correct answer. Which one?
A) the vertex is (-3,3), the focus is (4,-3),and the directrix is x=2
B) the vertex is (3,-3), the focus is (-4,3),and the directrix is x=2
C) the vertex is (3,-3), the focus is (4,-3),and the directrix is x=2
D) the vertex is (-3,3), the focus is (-4,3),and the directrix is x=-2
E)the vertex is (3,-3), the focus is (4,-3),and the directrix is x=-2
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
Basic vertex form:
In that form, the vertex is (h,k), and p is the directed distance (i.e., could be negative) from the directrix to the focus and from the focus to the vertex. The y term is squared, so the parabola opens right or left.
In your example, the vertex (h,k) is (3,-3); and 4p=4, so p=1. So the focus is 1 unit to the right of the vertex, at (4,-3); and the directrix is 1 unit to the left of the vertex, at x=2.
ANSWER: C)
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Side note:
I personally prefer the equivalent basic vertex form,
because I prefer having the linear expression on the left side of the equation.
But of course they are equivalent, so either form is fine.
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