document.write( "Question 84031: What is the vertex form of y=(3x+1)(x-2)and y=3(x-2)?
\n" ); document.write( "Is it y=3(x-5/6)^2-4.03? \n" ); document.write( "
Algebra.Com's Answer #60488 by Edwin McCravy(20055)\"\" \"About 
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document.write( "What is the vertex form of y=(3x+1)(x-2)\r\n" );
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document.write( "Foil it out\r\n" );
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document.write( "y = 3x² - 6x + x - 2\r\n" );
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document.write( "y = 3x² - 5x - 2\r\n" );
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document.write( "Factor the coefficient of x², which is 3,\r\n" );
document.write( "out of the first two terms only:  Not to \r\n" );
document.write( "take 3 out of -5x you divide -5 by 3 and get\r\n" );
document.write( "\"-5%2F3\"\r\n" );
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document.write( "y = 3(x² - \"5%2F3\"x) - 2\r\n" );
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document.write( "Take one-half the coefficient of x:\r\n" );
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document.write( "\"1%2F2\"·\"5%2F3\" = \"5%2F6\"\r\n" );
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document.write( "Then square what you get:\r\n" );
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document.write( "\"%285%2F6%29%5E2\" = \"25%2F36\"\r\n" );
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document.write( "Add that and then subtract it inside the parentheses:\r\n" );
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document.write( "y = 3(x² - \"5%2F3\"x + \"25%2F36\" - \"25%2F36\") - 2\r\n" );
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document.write( "Change the parentheses to brackets so we can factor \r\n" );
document.write( "and put parentheses inside:\r\n" );
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document.write( "y = 3[x² - \"5%2F3\"x + \"25%2F36\" - \"25%2F36\"] - 2\r\n" );
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document.write( "Factor the first three terms inside the brackets:\r\n" );
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document.write( "y = 3[(x - \"5%2F6\")(x - \"5%2F6\") - \"25%2F36\"] - 2 \r\n" );
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document.write( "Write (x - \"5%2F6\")(x - \"5%2F6\") as (x - \"5%2F6\")²\r\n" );
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document.write( "y = 3[(x - \"5%2F6\")² - \"25%2F36\"] - 2\r\n" );
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document.write( "Now remove the brackets by distributing the 3 into the \r\n" );
document.write( "bracket, leaving the (x - \"5%2F6\")² intact.\r\n" );
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document.write( "y = 3(x - \"5%2F6\")² - 3·\"25%2F36\" - 2\r\n" );
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document.write( "Simplify the last two terms:\r\n" );
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document.write( "y = 3(x - \"5%2F6\")² - \"25%2F12\" - 2 \r\n" );
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document.write( "y = 3(x - \"5%2F6\")² - \"25%2F12\" - \"24%2F12\"\r\n" );
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document.write( "y = 3(x - \"5%2F6\")² - \"49%2F12\"\r\n" );
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document.write( "Compare that to:\r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "and equate like parts of the two equations:\r\n" );
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document.write( "a = 3,\r\n" );
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document.write( "-h = \"-5%2F6\", so h = \"5%2F6\"\r\n" );
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document.write( "k = \"-49%2F12\"\r\n" );
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document.write( "So the vertex is the point (\"5%2F6\", \"-49%2F12\"), or\r\n" );
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document.write( "like (.8, 4.1)\r\n" );
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document.write( "or a mixed fraction is better for graphing:\r\n" );
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document.write( "The vertex is the point (\"5%2F6\", -(4\"1%2F12\")\r\n" );
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document.write( "Nasty fractions, indeed, but nasty fractions don't bother \r\n" );
document.write( "computers, so why should they bother us humans?  :-)\r\n" );
document.write( "But if we can get some more points we can plot the graph.\r\n" );
document.write( "The graph will be a parabola and we can observe if that\r\n" );
document.write( "point really and truly is the vertex: \r\n" );
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document.write( "We can get the y-intercept by going back to the original\r\n" );
document.write( "equation  y=(3x+1)(x-2) and substituting x=0. We get\r\n" );
document.write( "y = (3·0+1)(0-2) = (0+1)(-2) = (1)(-2) = -2\r\n" );
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document.write( "So we plot those two points and a bunch of others, we get\r\n" );
document.write( "this graph.  \r\n" );
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document.write( "     \r\n" );
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document.write( "Edwin
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