SOLUTION: -3(x+1/2)^2=y whats its focus, directrix, and vertex?

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Question 981055: -3(x+1/2)^2=y
whats its focus, directrix, and vertex?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
%28-1%2F3%29y=%28x%2B1%2F2%29%5E2
Compare this to 4py=%28x-h%29%5E2.

Yours has 4p=-1%2F3
p=-1%2F12.

The directrix is 1%2F12 units away from the vertex and is on the convex side of the vertex (0,-1/2). Focus is 1%2F12 units below the vertex. The parabola is vertical and opens downward.

Focus: y=-1%2F2-1%2F12=-6%2F12-1%2F12=-7%2F12, or (0, -7/12).
Directrix: The line y=-1%2F2%2B1%2F12=-5%2F12 or y=-5%2F12.
Vertex: ( 0,-1/2).

Refer in your book to the derivation of a parabola equation for horizontal directrix with focus on the x-axis; and that p is the distance from either focus or directrix.

graph%28250%2C250%2C-3%2C3%2C-3%2C3%2C-3%28x%2B1%2F2%29%5E2%29