Question 813137
Find the vertex, focus, and directrix of the parabola.{{{(1/2)x^2+2x=2y+4}}}
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1/2)x^2+2x=2y+4
complete the square:
(1/2)(x^2+4x+4)=2y+4+2
(1/2)(x+2)^2=2y+6
(x+2)^2=4y+12
(x+2)^2=4(y+3)
This is a parabola that opens up.
Its basic form of equation: (x-h)^2=4p(y-k)^2,(h,k)=(x,y) coordinates of the vertex.
vertex: (-2,-3)
axis of symmetry: x=-2
4p=4
p=1
focus:(-2,-2)(p-distance above vertex on the axis of symmetry)
directrix:y=-4(p-distance below vertex on the axis of symmetry)