SOLUTION: what are the vertex, focus and directrix of the parabola: 12y=x^2-6x+45? (x-3)^2=12(y-3) vertex is (3,3)???? or (-3,-3)??? Not sure how to get focus or directrix.

Question 710137: what are the vertex, focus and directrix of the parabola: 12y=x^2-6x+45?
(x-3)^2=12(y-3)
vertex is (3,3)???? or (-3,-3)???
Not sure how to get focus or directrix.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what are the vertex, focus and directrix of the parabola:
12y=x^2-6x+45
x^2-6x=12y-45
complete the square:
(x^2-6x+9)=12y-45+9
(x-3)^2=12y-36

This is an equation of a parabola that opens upwards.
Its standard form: , (h,k)=(x,y) coordinates of the vertex.
For given parabola:
vertex: (3,3)
axis of symmetry: x=3
4p=12
p=4
focus: (3,7) (p-distance above vertex on the axis of symmetry)
directrix: y=-1 (p-distance below vertex on the axis of symmetry)

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