document.write( "Question 126439: 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 #92655 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Identify the axis of symmetry, create a suitable table of values, then sketch the graph (including the axis of symmetry).
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document.write( "First make the table:\r\n" );
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document.write( "x|-1| 0| 1| 2| 3| 4\r\n" );
document.write( "y|-7|-3|-1|-1|-3|-7\r\n" );
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document.write( "Then we'll plot those points\r\n" );
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document.write( "Next we'll calculate the axis of symmetry:\r\n" );
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document.write( "Rule:\r\n" );
document.write( "The axis of syymetry of the graph whose equation is\r\n" );
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document.write( "y = Ax² + Bx + C\r\n" );
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document.write( "is the vertical line whose equation is \r\n" );
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document.write( "x = \"-B%2F%282A%29\"\r\n" );
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document.write( "You may not have learned about the vertex, but I'll\r\n" );
document.write( "throw that in too.\r\n" );
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document.write( "Rule:\r\n" );
document.write( "The vertex is the point\r\n" );
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document.write( "(\"-B%2F%282A%29\", \"-D%2F%284A%29\"), where D = B²-4AC\r\n" );
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document.write( "(D is called the \"discriminant\")\r\n" );
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document.write( "So in the case of \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 \r\n" );
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document.write( "so the axis of symmetry is the vertical line\r\n" );
document.write( "whose equation is\r\n" );
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document.write( "x = \"-B%2F%282A%29\"\r\n" );
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document.write( "or\r\n" );
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document.write( "x = \"-%283%29%2F%282%28-1%29%29\"\r\n" );
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document.write( "x = \"-3%2F%28-2%29\"\r\n" );
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document.write( "x = \"3%2F2\"\r\n" );
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document.write( "So we'll sketch in the\r\n" );
document.write( "axis of symmetry:\r\n" );
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document.write( "and to find the vertex,\r\n" );
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document.write( "D = B² - 4AC\r\n" );
document.write( "D = 3² - 4(-1)(-3)\r\n" );
document.write( "D = 9 - 12\r\n" );
document.write( "D = -3\r\n" );
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document.write( "So the vertex is the point\r\n" );
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document.write( "(\"-B%2F%282A%29\", \"-D%2F%284A%29\" or\r\n" );
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document.write( "(\"3%2F2\", \"-%28-3%29%2F%284%28-1%29%29\", or\r\n" );
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document.write( "(\"3%2F2\", \"3%2F%28-4%29\", or\r\n" );
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document.write( "(\"3%2F2\", \"-3%2F4\"),  \r\n" );
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document.write( "So we'll plot the vertex point too:\r\n" );
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document.write( "Now we'll sketch in the graph, which is\r\n" );
document.write( "a parabola:\r\n" );
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document.write( "  \r\n" );
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document.write( "Edwin
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