document.write( "Question 88054: determine the range for:f(x)=9-8x-x^2 \n" ); document.write( "
Algebra.Com's Answer #64000 by Edwin McCravy(20059) $\"\"$ $\"About$
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document.write( "determine the range for:f(x)=9-8x-xｲ\r\n" );
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document.write( "To do it graphically, draw the graph by plotting points.\r\n" );
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document.write( "And you can see that the highest point is (-4,25)\r\n" );
document.write( "and so the values of y are never less than 25, so the\r\n" );
document.write( "range is (-oo, 25]\r\n" );
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document.write( "Replace f(x) by y\r\n" );
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document.write( "              y = 9 - 8x - xｲ\r\n" );
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document.write( "Solve for x\r\n" );
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document.write( "xｲ + 8x + y - 9 = 0\r\n" );
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document.write( "xｲ + 8x + (y-9) = 0\r\n" );
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document.write( "Use the quadratic formula:\r\n" );
document.write( "                  ______ \r\n" );
document.write( "            -b ｱ ﾖbｲ-4ac\r\n" );
document.write( "        x = 覧覧覧覧覧覧予r\n" );
document.write( "                2a \r\n" );
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document.write( "where a = 1; b = 8; c = (y-9)\r\n" );
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document.write( "                     ______________\r\n" );
document.write( "             -(8) ｱ ﾖ(8)ｲ-4(1)(y-9)\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧覧覧覧覧覧\r\n" );
document.write( "                     2(1)\r\n" );
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document.write( "                   ________                 \r\n" );
document.write( "             -8 ｱ ﾖ64-4y+36\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧覧予r\n" );
document.write( "                    2\r\n" );
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document.write( "                   ______                \r\n" );
document.write( "             -8 ｱ ﾖ100-4y\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧\r\n" );
document.write( "                   2\r\n" );
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document.write( "                   ______                \r\n" );
document.write( "             -8 ｱ ﾖ4(25-y)\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧\r\n" );
document.write( "                   2\r\n" );
document.write( "                    ____\r\n" );
document.write( "             -8 ｱ 2ﾖ25-y\r\n" );
document.write( "        x = 覧覧覧覧覧覧覧\r\n" );
document.write( "                  2\r\n" );
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document.write( "                      ____\r\n" );
document.write( "             -8     2ﾖ25-y\r\n" );
document.write( "        x = 覧覧 ｱ 覧覧覧覧覧\r\n" );
document.write( "              2        2\r\n" );
document.write( "                  ____ \r\n" );
document.write( "        x = -4 ｱ ﾖ25-y\r\n" );
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document.write( "What's under the radical cannot be negative.\r\n" );
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document.write( "Therefore\r\n" );
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document.write( "25-y > 0\r\n" );
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document.write( "  -y > -25\r\n" );
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document.write( "   y < 25\r\n" );
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document.write( "Or in interval notation (-oo, 25]  \r\n" );
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document.write( "Edwin
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