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Question 545587: put in standard form and graph x^2-2x+y+7
find the focus and directrix
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! put in standard form and graph x^2-2x+y+7
find the focus and directrix
**
x^2-2x+y+7=0
y=-x^2+2x-7
complete the square
y=-(x^2-2x+1)-7+1
y=-(x-1)^2-6
(x-1)^2=-(y+6)
This equation is in standard form for a parabola: (x-h)^2=4p(y-k), with (h,k) being the (x,y) coordinates of the vertex. Parabola opens downwards.
For given equation:(x-1)^2=-(y+6)
vertex: (1,-6)
axis of symmetry: x=1
4p=1
p=1/4
Focus and directrix are p units from the vertex on the axis of symmetry
Focus: (1, -6+p)=(1,-6-1/4)=1,-25/4)
Directrix: y=-6+1/4=-23/4
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