document.write( "Question 545209: 0=y^2-8x+4y-20 ive tried everything but i can't get the answer. its asking for the equation in standard form,vertex,focus,directrix,and the functions in terms of y. \n" ); document.write( "

Algebra.Com's Answer #355535 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "The standard form is\r\n" );
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document.write( "(y-k)² = 4p(x-h)\r\n" );
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document.write( "                0 = y² - 8x + 4y - 20\r\n" );
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document.write( "y² - 8x + 4y - 20 = 0\r\n" );
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document.write( "          y² + 4y = 8x + 20\r\n" );
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document.write( "Multiply the coefficient of y, which is 4, by , getting 2\r\n" );
document.write( "Then square 2, getting 4, and add 4 to both sides:\r\n" );
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document.write( "      y² + 4y + 4 = 8x + 20 + 4\r\n" );
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document.write( "   (y + 2)(y + 2) = 8x + 24\r\n" );
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document.write( "         (y + 2)² = 4(x + 3)\r\n" );
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document.write( "Compare to the standard form:\r\n" );
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document.write( "         (y - k)² = 4p(x - h)\r\n" );
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document.write( "So the vertex is (h,k) = (-3,-2), 4p = 4, so p = 1\r\n" );
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document.write( "Since p is positive, the parabola opens right.  Since p = 1,\r\n" );
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document.write( "The focus is a point 1 unit to the right of the vertex (-2,-2),\r\n" );
document.write( "and the directrix is a vertical line 1 unit left of the vertex, \r\n" );
document.write( "so its equation is x = -4, the green line:\r\n" );
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document.write( "Edwin

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