document.write( "Question 1078317: The equation of a parabola is given. \r
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Algebra.Com's Answer #692827 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"y\"\"%22%22=%22%22\"\"expr%28-1%2F12%29x%5E2-2x-1\"\r\n" );
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document.write( "First get into standard form, which is\r\n" );
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document.write( "\"%28x-h%29%5E2\"\"%22%22=%22%22\"\"4p%28y-k%29\"\r\n" );
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document.write( "Then the vertex is (h,k), the focus is (h,k+p),\r\n" );
document.write( "and the equation of the directrix is y=k-p\r\n" );
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document.write( "Instead of doing your homework for you, I'll\r\n" );
document.write( "do one exactly like it.  Then you can use it \r\n" );
document.write( "as a model to do yours step by step\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"expr%28-1%2F20%29x%5E2-2x-10\"\r\n" );
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document.write( "Clear of fractions by multiplying through by 20\r\n" );
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document.write( "\"20y\"\"%22%22=%22%22\"\"-x%5E2-40x-200\"\r\n" );
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document.write( "Get the x terms on the left side\r\n" );
document.write( "and all the other terms on the right\r\n" );
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document.write( "\"x%5E2%2B40x\"\"%22%22=%22%22\"\"-20y-200\"\r\n" );
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document.write( "Complete the square on the left:\r\n" );
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document.write( "1. Multiply the coefficient of x, which is 40, by 1/2, getting 20\r\n" );
document.write( "2. Square what you got, 202=400\r\n" );
document.write( "3. Add that, 400, to both sides of the equation\r\n" );
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document.write( "\"x%5E2%2B40x%2B400\"\"%22%22=%22%22\"\"-20y-200%2B400\"\r\n" );
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document.write( "Factor the left side as (x+20)(x+20) and write it as (x+20)2\r\n" );
document.write( "Combine the -200+400 on the right as +200\r\n" );
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document.write( "\"%28x%2B20%29%5E2\"\"%22%22=%22%22\"\"-20y%2B200\"\r\n" );
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document.write( "Factor out the coefficient of y, which is -20 on the right,\r\n" );
document.write( "remembering that when you factor out a negative, you get\r\n" );
document.write( "a sign change inside the parentheses:\r\n" );
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document.write( "\"%28x%2B20%29%5E2\"\"%22%22=%22%22\"\"-20%28y-10%29\"\r\n" );
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document.write( "Compare that to\r\n" );
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document.write( "\"%28x-h%29%5E2\"\"%22%22=%22%22\"\"4p%28y-k%29\"\r\n" );
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document.write( "where the vertex is (h,k), the focus is (h,k+p),\r\n" );
document.write( "and the equation of the directrix is y=k-p\r\n" );
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document.write( "So h = -20, 4p = -20, k=10.\r\n" );
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document.write( "And since 4p =-20, p = -5.\r\n" );
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document.write( "So the vertex is (-20,10), the focus is (-20,10-5) or (-20,5)\r\n" );
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document.write( "(-20,5)  <-- focus\r\n" );
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document.write( "and the equation of the directrix is y=10-(-5) or y = 15 \r\n" );
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document.write( "Now you can do yours exactly the same way step by step.\r\n" );
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document.write( "Edwin
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