document.write( "Question 884464: What is the vertex, focus, axis of symmetry, and directrix for the parabola whose equation is y2+8y+48x-32=0 \n" ); document.write( "

Algebra.Com's Answer #534412 by lwsshak3(11628) $\"\"$ $\"About$

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What is the vertex, focus, axis of symmetry, and directrix for the parabola whose equation is y2+8y+48x-32=0
\n" ); document.write( "complete the square:
\n" ); document.write( "(y2+8y+16)+48x=32+16
\n" ); document.write( "(y+4)^2=-48x+48
\n" ); document.write( "(y+4)^2=-48(x-1)
\n" ); document.write( "This is an equation of a parabola that opens leftward.
\n" ); document.write( "Its basic form of equation: $\"%28y-k%29%5E2=-4p%28x-h%29\"$ , (h,k)=coordinates of the vertex
\n" ); document.write( "For given equation:
\n" ); document.write( "vertex: (1,-4)
\n" ); document.write( "axis of symmetry: y=-4
\n" ); document.write( "4p=48
\n" ); document.write( "p=12
\n" ); document.write( "focus: (-11,-4) (p-distance left of vertex on the axis of symmetry)
\n" ); document.write( "directrix: x=13 (p-distance right of vertex on the axis of symmetry) \n" ); document.write( "

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