document.write( "Question 854644: Find the vertex, focus, and directrix of the parabola. Graph the equation.
\n" ); document.write( "y^2 - 2y = 8x - 1 \n" ); document.write( "

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Find the vertex, focus, and directrix of the parabola. Graph the equation.
\n" ); document.write( "y^2 - 2y = 8x - 1
\n" ); document.write( "complete the square:
\n" ); document.write( "(y^2-2y+1) = 8x - 1+1
\n" ); document.write( "(y-1)^2=8x
\n" ); document.write( "This is an equation of a parabola that opens right.
\n" ); document.write( "Its basic form of equation: (y-k)^2=4p(x-h)^2, (h,k)=coordinates of the vertex
\n" ); document.write( "For given parabola:
\n" ); document.write( "vertex: (0,1)
\n" ); document.write( "axis of symmetry: y=1
\n" ); document.write( "4p=8
\n" ); document.write( "p=2
\n" ); document.write( "focus: (2,1) (p-distance to the right of vertex on the axis of symmetry)
\n" ); document.write( "directrix: x=-2 (p-distance to the left of vertex on the axis of symmetry)\r
\n" ); document.write( "\n" ); document.write( "see graph below:
\n" ); document.write( "y=(8x)^.5+1
\n" ); document.write( " $\"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%288x%29%5E.5%2B1%2C-%288x%29%5E.5%2B1%29+\"$ \n" ); document.write( "

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