document.write( "Question 39844: Solve the following equation so that it can be plotted on a graphing calculator.
\n" ); document.write( "4x^2 - 2xy + 3y^2 =2. I know it should be able able to use the quadratic formula but every way I try, I do not get the right answer. The question came from the TeXeS Review manual. There is no ISBN. \n" ); document.write( "
Algebra.Com's Answer #25279 by AnlytcPhil(1806)\"\" \"About 
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Solve the following equation so that it can be plotted on a graphing calculator.\r\n" );
document.write( "4x^2 - 2xy + 3y^2 =2. I know it should be able able to use the quadratic\r\n" );
document.write( "formula but every way I try, I do not get the right answer. The question came\r\n" );
document.write( "from the TeXeS Review manual. There is no ISBN.\r\n" );
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document.write( "4xｲ - 2xy + 3yｲ = 2\r\n" );
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document.write( "Rearrange it in descending order of powers of y with 0 on the right:\r\n" );
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document.write( "3yｲ - 2xy + 4xｲ - 2 = 0\r\n" );
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document.write( "Write it this way, to see what A, B, and C are.\r\n" );
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document.write( "(3)yｲ + (-2x)y + (4xｲ-2) = 0\r\n" );
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document.write( "Then for the quadratic formula,\r\n" );
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document.write( "A = (3),  B = (-2x),  C = (4xｲ-2)\r\n" );
document.write( "           ________\r\n" );
document.write( "     -B ｱ ﾖBｲ - 4AC\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧予r\n" );
document.write( "           2A\r\n" );
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document.write( "               ____________________\r\n" );
document.write( "     -(-2x) ｱ ﾖ(-2x)ｲ - 4(3)(4xｲ-2)\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "                2(3)\r\n" );
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document.write( "You can put that in the TI-83 just like this without simplifying further:\r\n" );
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document.write( "Y1 = (-(-2X) + ﾖ((-2X)ｲ - 4(3)(4Xｲ-2)))/(2(3))\r\n" );
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document.write( "Y2 = (-(-2X) - ﾖ((-2X)ｲ - 4(3)(4Xｲ-2)))/(2(3))\r\n" );
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document.write( "use window Xmin = -1, Xmax = 1, Xscl = 1, Ymin = -1, Ymax = 1, Yscl=1, Xres=1\r\n" );
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document.write( "You get a slanted ellipse\r\n" );
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document.write( "or you can simplify it further first\r\n" );
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document.write( "               ____________________\r\n" );
document.write( "     -(-2x) ｱ ﾖ(-2x)ｲ - 4(3)(4xｲ-2)\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "                2(3)\r\n" );
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document.write( "           _______________\r\n" );
document.write( "     2x ｱ ﾖ4xｲ - 12(4xｲ-2)\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "                6\r\n" );
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document.write( "           _______________\r\n" );
document.write( "     2x ｱ ﾖ4xｲ - 48xｲ + 24\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "                6\r\n" );
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document.write( "           ___________\r\n" );
document.write( "     2x ｱ ﾖ-44xｲ + 24\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "             6\r\n" );
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document.write( "           ___________\r\n" );
document.write( "     2x ｱ ﾖ4(-11xｲ + 6\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "             6\r\n" );
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document.write( "            ___________\r\n" );
document.write( "     2x ｱ 2ﾖ(-11xｲ + 6\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "             6\r\n" );
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document.write( "            __________\r\n" );
document.write( "     2[x ｱ ﾖ-11xｲ + 6\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧覧予r\n" );
document.write( "             6\r\n" );
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document.write( "Cancel the 2 into the 6\r\n" );
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document.write( "          _________\r\n" );
document.write( "     x ｱ ﾖ-11xｲ + 6\r\n" );
document.write( "y = 覧覧覧覧覧覧覧覧予r\n" );
document.write( "            3\r\n" );
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document.write( "          ________\r\n" );
document.write( "     x ｱ ﾖ6 - 11xｲ \r\n" );
document.write( "y = 覧覧覧覧覧覧覧予r\n" );
document.write( "            3\r\n" );
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document.write( "Then you can enter it in the TI-83 as\r\n" );
document.write( "            \r\n" );
document.write( "Y1 = (X + ﾖ(6 - 11Xｲ))/3\r\n" );
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document.write( "Y2 = (X - ﾖ(6 - 11Xｲ))/3\r\n" );
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document.write( "Either way you get this slanted ellipse.\r\n" );
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document.write( "Edwin
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