document.write( "Question 615650: How do you find the equation, vertex, focus, directrix, and latus rectum of the following:\r
\n" ); document.write( "\n" ); document.write( "-14x+2y^2-8y=20 \n" ); document.write( "
Algebra.Com's Answer #387278 by lwsshak3(11628)\"\" \"About 
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How do you find the equation, vertex, focus, directrix, and latus rectum of the following:
\n" ); document.write( "-14x+2y^2-8y=20
\n" ); document.write( "complete the square
\n" ); document.write( "2(y^2-4y+4)=20+14x+8
\n" ); document.write( "2(y-2)^2=14x+28
\n" ); document.write( "divide by 2
\n" ); document.write( "(y-2)^2=7x+14
\n" ); document.write( "(y-2)^2=7(x+2)
\n" ); document.write( "This is an equation of a parabola that opens rightwards.
\n" ); document.write( "Its standard form: (y-k)^2=4px, (h,k)=(x,y) coordinates of the vertex
\n" ); document.write( "For given equation:(y-2)^2=7(x+2)
\n" ); document.write( "vertex:(-2,2)
\n" ); document.write( "axis of symmetry: y=2
\n" ); document.write( "4p=7
\n" ); document.write( "p=7/4
\n" ); document.write( "Focus: (-2+p,2)=(-2+7/4,2)=(-1/4,2) (p distance to the right of the vertex on the axis of symmetry)
\n" ); document.write( "Directrix: x=(-2-p)=(-2-7/4)=-15/4 (p distance to the left of the vertex on the axis of symmetry)
\n" ); document.write( "latus rectum:
\n" ); document.write( "length of latus rectum=4p=7
\n" ); document.write( "2p=7/2
\n" ); document.write( "end points: (-1/4,2±2p)
\n" ); document.write( "=(-1/4,2±7/2)
\n" ); document.write( "=(-1/4,-1.5) and (-1/4,5.5)\r
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