document.write( "Question 710137: what are the vertex, focus and directrix of the parabola: 12y=x^2-6x+45?
\n" ); document.write( "(x-3)^2=12(y-3)
\n" ); document.write( "vertex is (3,3)???? or (-3,-3)???
\n" ); document.write( "Not sure how to get focus or directrix. \n" ); document.write( "

Algebra.Com's Answer #437735 by lwsshak3(11628) $\"\"$ $\"About$

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what are the vertex, focus and directrix of the parabola:
\n" ); document.write( "12y=x^2-6x+45
\n" ); document.write( "x^2-6x=12y-45
\n" ); document.write( "complete the square:
\n" ); document.write( "(x^2-6x+9)=12y-45+9
\n" ); document.write( "(x-3)^2=12y-36
\n" ); document.write( " $\"%28x-3%29%5E2=12%28y-3%29\"$
\n" ); document.write( "This is an equation of a parabola that opens upwards.
\n" ); document.write( "Its standard form: $\"%28x-h%29%5E2=4p%28y-k%29\"$ , (h,k)=(x,y) coordinates of the vertex.
\n" ); document.write( "For given parabola:
\n" ); document.write( "vertex: (3,3)
\n" ); document.write( "axis of symmetry: x=3
\n" ); document.write( "4p=12
\n" ); document.write( "p=4
\n" ); document.write( "focus: (3,7) (p-distance above vertex on the axis of symmetry)
\n" ); document.write( "directrix: y=-1 (p-distance below vertex on the axis of symmetry)
\n" ); document.write( " \n" ); document.write( "

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