document.write( "Question 893609: Find the vertex, focus, directrix, and focal width of the parabola. -2x^2+20x-y-52=0 \n" ); document.write( "

Algebra.Com's Answer #542180 by lwsshak3(11628) $\"\"$ $\"About$

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Find the vertex, focus, directrix, and focal width of the parabola.
\n" ); document.write( "-2x^2+20x-y-52=0
\n" ); document.write( "complete the square:
\n" ); document.write( "-2(x^2-10x+25)=y+52-50
\n" ); document.write( "-2(x-5)^2=y+2
\n" ); document.write( "(x-5)^2=-(1/2)(y+2)
\n" ); document.write( "This is an equation of a parabola that opens downward.
\n" ); document.write( "Ita basic form of equation: (x-h)^2=-4p(y-k)
\n" ); document.write( "For given parabola:
\n" ); document.write( "4p=1/2
\n" ); document.write( "p=1/8
\n" ); document.write( "vertex:(5,-2)
\n" ); document.write( "axis of symmetry: x=5
\n" ); document.write( "focus:(5,-17/8)(p-distance below vertex on the axis of symmetry)
\n" ); document.write( "directrix:-15/8 (p-distance above vertex on the axis of symmetry)
\n" ); document.write( "focal width=4p=1/2
\n" ); document.write( " \n" ); document.write( "

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