Question 881139: I need to identify the focus, vertex, directrix, and graph x=-2y^2+4y-3
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! identify the focus, vertex, directrix, and graph
x=-2y^2+4y-3
complete the square:
x=-2(y^2-2y+1)+2-3
x=-2(y-1)^2-1
(x+1)=-2(y-1)^2
(y-1)^2=-(1/2)(x+1)
This is an equation of a parabola that opens leftward.
Its basic form of equation: (y-k)^2=-4p(x-h), (h,k)=coordinates of the vertex
vertex:(-1,1)
4p=1/2
p=1/8
focus: (-9/8,1)
directrix: x=-7/8
..
see graph below:
y=±(-(x+1)/2)^.5+1
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