document.write( "Question 1181193: Find the number in the interval [ - 2, 2 ] so that the difference of the
\n" ); document.write( "number from its square is maximized. \n" ); document.write( "
Algebra.Com's Answer #811074 by Edwin McCravy(20077)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let x be the number in the interval [-2, 2] so that the difference of the\r\n" );
document.write( "number from its square is maximized. \r\n" );
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document.write( "the difference of the number x from its square x2 is x2 - x.\r\n" );
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document.write( "Let y equal to this difference x2 - x.\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"x%5E2-x\"\r\n" );
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document.write( "The graph of the equation looks like this\r\n" );
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document.write( "\"graph%28400%2C400%2C-3%2C3%2C-3%2C3%2Cx%5E2-x%29\"\r\n" );
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document.write( "The value of y (the difference) is minimized at the bottom of\r\n" );
document.write( "that graph (at the bottom point), which is the vertex.\r\n" );
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document.write( "The formula for the x-coordinate of the vertex of \"y=ax%5E2%2Bbx%2Bc\" is \r\n" );
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document.write( "     \"-b%2F%282%2Aa%29\"\r\n" );
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document.write( "\"y=x%5E2-x\" can be thought of as \"y=1a%5E2-1x%2B0\" so a=1, b=-1, c=0\r\n" );
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document.write( "     \"-b%2F%282a%29\"\r\n" );
document.write( "     \"-%28-1%29%2F%282%281%29%29\"\r\n" );
document.write( "     \"1%2F2\"\r\n" );
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document.write( "So 1/2 is the number in the interval [-2, 2] so that the difference of the\r\n" );
document.write( "number from its square is maximized. \r\n" );
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document.write( "Edwin
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