document.write( "Question 1101490: parabola- sketch the parabola (y-1)^2 = 8(x-2) showing clearly all points and labeling, marking clearly the directrix, focus and vertex. \n" ); document.write( "

Algebra.Com's Answer #716119 by greenestamps(13334) $\"\"$ $\"About$

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\n" ); document.write( "With the y variable squared, this parabola opens horizontally; with the coefficient on the x term positive, it opens to the right.

\n" ); document.write( "The standard vertex form (that I use!) for a parabola that opens horizontally is

\n" ); document.write( " $\"%28x-h%29+=+%281%2F%284p%29%29%28y-k%29%5E2%29\"$

\n" ); document.write( "or

\n" ); document.write( " $\"%28y-k%29%5E2+=+4p%28x-h%29\"$

\n" ); document.write( "In this form, p is the distance from the vertex to the focus, and from the vertex to the directrix.

\n" ); document.write( "The equation for your parabola is
\n" ); document.write( " $\"%28y-1%29%5E2+=+8%28x-2%29\"$

\n" ); document.write( "That means p is 2; so the vertex of the parabola is at (2,1); the focus is 2 units to the right of the vertex, at (4,1); and the directrix is the vertical line 2 units to the left of the vertex, x=0.

\n" ); document.write( "

\n" ); document.write( "(Sorry.... I haven't yet figured out how to do labeling on a graph....) \n" ); document.write( "

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