document.write( "Question 145226: What is the directrix of the parabola with the equation y+3= 1/10 (x+2)^2? \n" ); document.write( "
Algebra.Com's Answer #105973 by Edwin McCravy(20062)\"\" \"About 
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What is the directrix of the parabola with the equation y+3= 1/10 (x+2)^2?
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document.write( "What you have to know about parabolas in standard form:\r\n" );
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document.write( "1: Parabolas whose equations are in the standard form\r\n" );
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document.write( "\"%28x-h%29%5E2+=+4p%28y-k%29\"\r\n" );
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document.write( "opens upward if \"p+%3E+0\" and downward if \"p+%3C+0\"\r\n" );
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document.write( "They have vertex (h, k), focus (h, k+p), and\r\n" );
document.write( "the directrix is the horizontal line whose equation\r\n" );
document.write( "is y=k-p\r\n" );
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document.write( "2: Parabolas whose equations are in the standard form\r\n" );
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document.write( "\"%28y-k%29%5E2+=+4p%28x-h%29\"\r\n" );
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document.write( "opens rightward if \"p+%3E+0\" and leftward if \"p+%3C+0\"\r\n" );
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document.write( "They have vertex (h, k), focus (h+p, k), and\r\n" );
document.write( "the directrix is the vertical line whose equation\r\n" );
document.write( "is x=h-p.\r\n" );
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document.write( "Your equation\r\n" );
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document.write( "\"y%2B3=+%281%2F10%29+%28x%2B2%29%5E2\"\r\n" );
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document.write( "can be placed in the standard form 1.\r\n" );
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document.write( "Multiply both sides by 10\r\n" );
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document.write( "\"10%28y%2B3%29=+10%2A%281%2F10%29%28x%2B2%29%5E2\"\r\n" );
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document.write( "\"10%28y%2B3%29=+cross%2810%29%2A%281%2Fcross%2810%29%29%28x%2B2%29%5E2\"\r\n" );
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document.write( "\"10%28y%2B3%29=+%28x%2B2%29%5E2\"\r\n" );
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document.write( "Swap sides:\r\n" );
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document.write( "\"%28x%2B2%29%5E2=10%28y%2B3%29\"\r\n" );
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document.write( "Compare to the standard equation in 1 above:\r\n" );
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document.write( "\"%28x-h%29%5E2+=+4p%28y-k%29\"\r\n" );
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document.write( "So \"-h=2\" so \"h=-2\",\r\n" );
document.write( "\"4p=10\" so \"p=10%2F4=5%2F2\"\r\n" );
document.write( "\"-k=3\" so \"k=-3\"\r\n" );
document.write( "opens upward because \"p+=+5%2F2+%3E+0\" \r\n" );
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document.write( "It has vertex (h, k) = (-2,-3)\r\n" );
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document.write( "It has focus (h, k+p) = (-2,-3+\"5%2F2\") = (-2, \"-1%2F2\")\r\n" );
document.write( "the directrix is the horizontal line whose equation\r\n" );
document.write( "is \"y=k-p\" or \"y+=+-3-%285%2F2%29\" or \"y+=+-11%2F2\"\r\n" );
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document.write( "To draw the graph, plot the focus (-2, \"-1%2F2\"), the vertex(-2,-3) and\r\n" );
document.write( "the directrix \"y=-11%2F2\"\r\n" );
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document.write( "Draw a line from the focus directly to the directrix. The\r\n" );
document.write( "vertex should be the midpoint of this line.\r\n" );
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document.write( "Draw a square with that line being its left side:\r\n" );
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document.write( "Draw another square with that line being its right side:\r\n" );
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document.write( "Finally, draw the parabola through the vertex and the\r\n" );
document.write( "upper corners of the two squares:\r\n" );
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document.write( "Edwin
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