SOLUTION: identify the vertex, focus and directrix. Then sketch the graph x= -1/4y^2+1/2y-9/4

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Question 560429: identify the vertex, focus and directrix. Then sketch the graph
x= -1/4y^2+1/2y-9/4
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
identify the vertex, focus and directrix. Then sketch the graph
x= -1/4y^2+1/2y-9/4
This is an equation of a parabola with standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
complete the square
x=-1/4(y^2-2y+1)-9/4+1/4
x=-1/4(y-1)^2-2
(x+2)=-1/4(y-1)^2
(y-1)^2=-4(x+2)
vertex: (-2,1)
Axis of symmetry: y=1, parabola opens leftwards
4p=4
p=1
Focus: (-3,1) (p-distance from vertex on axis of symmetry)
Directrix: x=-1 (perpendicular to axis of symmetry and p-distance from vertex on axis of symmetry.
see graph below:
y=±(-4x-8)^.5+1