document.write( "Question 52344This question is from textbook Beginnning Algebra
\n" ); document.write( ": Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).\r
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Algebra.Com's Answer #34868 by AnlytcPhil(1806) $\"\"$ $\"About$

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document.write( "Identify the axis of symmetry, create a suitable \r\n" );
document.write( "table of values, then sketch the graph \r\n" );
document.write( "(including the axis of symmetry).\r\n" );
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document.write( "y = –x² + 3x – 3\r\n" );
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document.write( "For the quadratic equation \r\n" );
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document.write( "y = Ax² + Bx + C the axis of symmetry has the \r\n" );
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document.write( "x = -B/(2A)\r\n" );
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document.write( "In your problem,\r\n" );
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document.write( "y = –x² + 3x – 3,\r\n" );
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document.write( "A = -1, B = 3, C = -3, so the axis of symmetry has\r\n" );
document.write( "the equation\r\n" );
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document.write( "x = -B/[2A]\r\n" );
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document.write( "x = -(3)/[2(-1)]\r\n" );
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document.write( "x = 3/2\r\n" );
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document.write( "First let's graph the axis of symmetry.  We have \r\n" );
document.write( "just one choice for x, namely 3/2.  We just choose \r\n" );
document.write( "arbitrary values for y, always choosing 3/2 for x, \r\n" );
document.write( "and draw the graph of the the axis of symmetry:\r\n" );
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document.write( "AXIS OF SYMMETRY\r\n" );
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document.write( " x  |  y |   (x,y)  |\r\n" );
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document.write( "3/2 |  5 | (3/2, 5) |     \r\n" );
document.write( "3/2 |  3 | (3/2, 3) |       \r\n" );
document.write( "3/2 | -2 | (3/2,-2) |       \r\n" );
document.write( "3/2 |  6 | (3/2, 6) |        \r\n" );
document.write( "3/2 | -1 | (3/2, 1) |         \r\n" );
document.write( "3/2 |  4 | (3/2, 4) |\r\n" );
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document.write( "Those values for y are completely arbitrary!\r\n" );
document.write( "Plotting these points and drawing through them\r\n" );
document.write( "we get this graph, a vertical line\r\n" );
document.write( "(Notice that 3/2 is just 1 and a half).\r\n" );
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document.write( "Now we draw a graph of your quadratic equations:\r\n" );
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document.write( "y = –x² + 3x – 3\r\n" );
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document.write( "QUADRATIC EQUATION\r\n" );
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document.write( " x | y  |   (x,y)  |\r\n" );
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document.write( "-1 | -7 | (-1,-7) |     \r\n" );
document.write( " 0 | -3 |  (0,-3) |       \r\n" );
document.write( " 1 | -1 |  (1,-1) |       \r\n" );
document.write( " 2 | -1 |  (2,-1) |        \r\n" );
document.write( " 3 | -3 |  (3,-3) |         \r\n" );
document.write( " 4 | -7 |  (4,-7) |        \r\n" );
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document.write( "Now we plot those points and draw a\r\n" );
document.write( "smooth (green) curve through them:\r\n" );
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document.write( "You will notice that the graph of the axis of \r\n" );
document.write( "symmetry, which is the red vertical line, \r\n" );
document.write( "bisects the green graph into two symmetrical \r\n" );
document.write( "halves.  \r\n" );
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document.write( "Edwin McCravy

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