document.write( "Question 813137: Find the vertex, focus, and directrix of the parabola.\r
\n" ); document.write( "\n" ); document.write( " $\"%281%2F2%29x%5E2%2B2x=2y%2B4\"$ \n" ); document.write( "

Algebra.Com's Answer #489695 by lwsshak3(11628) $\"\"$ $\"About$

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Find the vertex, focus, and directrix of the parabola. $\"%281%2F2%29x%5E2%2B2x=2y%2B4\"$
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\n" ); document.write( "1/2)x^2+2x=2y+4
\n" ); document.write( "complete the square:
\n" ); document.write( "(1/2)(x^2+4x+4)=2y+4+2
\n" ); document.write( "(1/2)(x+2)^2=2y+6
\n" ); document.write( "(x+2)^2=4y+12
\n" ); document.write( "(x+2)^2=4(y+3)
\n" ); document.write( "This is a parabola that opens up.
\n" ); document.write( "Its basic form of equation: (x-h)^2=4p(y-k)^2,(h,k)=(x,y) coordinates of the vertex.
\n" ); document.write( "vertex: (-2,-3)
\n" ); document.write( "axis of symmetry: x=-2
\n" ); document.write( "4p=4
\n" ); document.write( "p=1
\n" ); document.write( "focus:(-2,-2)(p-distance above vertex on the axis of symmetry)
\n" ); document.write( "directrix:y=-4(p-distance below vertex on the axis of symmetry)\r
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