document.write( "Question 146893: Find the quadratic function that has a vertex at (-1,3) and whose graph passes through the point (2,1). \n" ); document.write( "
Algebra.Com's Answer #107285 by Edwin McCravy(20056)\"\" \"About 
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Find the quadratic function that has a vertex at (-1,3) and whose graph passes through the point (2,1).
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document.write( "All quadratic functions are in the form\r\n" );
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document.write( "\"f%28x%29=a%28x-h%29%5E2+%2B+k\"\r\n" );
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document.write( "or for convenience, let's write \"y\" for \"f%28x%29\"\r\n" );
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document.write( "\"y+=+a%28x-h%29%5E2%2Bk\"\r\n" );
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document.write( "where the vertex is (\"h\",\"k\").\r\n" );
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document.write( "So since the vertex is (\"-1\",\"3\"), we plug those in\r\n" );
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document.write( "\"y+=+a%28x-h%29%5E2%2Bk\"\r\n" );
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document.write( "\"y+=+a%28x-%28-1%29%29%5E2%2B3\"\r\n" );
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document.write( "\"y+=+a%28x%2B1%29%5E2%2B3\"\r\n" );
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document.write( "Now all we need is \"a\"\r\n" );
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document.write( "So we substitute (\"x\",\"y\") = (\"2\",\"1\").\r\n" );
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document.write( "\"y+=+a%28x%2B1%29%5E2%2B3\"\r\n" );
document.write( "\"1+=+a%282%2B1%29%5E2%2B3\"\r\n" );
document.write( "\"1+=+a%283%29%5E2%2B3\"\r\n" );
document.write( "\"1+=+9a%2B3\"\r\n" );
document.write( "\"-2=9a\"\r\n" );
document.write( "\"-2%2F9=a\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"y+=+a%28x%2B1%29%5E2%2B3\"\r\n" );
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document.write( "becomes\r\n" );
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document.write( "\"y+=+-2%2F9\"\"%28x%2B1%29%5E2%2B3\"\r\n" );
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document.write( "or\r\n" );
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document.write( "\"f%28x%29+=+-2%2F9\"\"%28x%2B1%29%5E2%2B3\"\r\n" );
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document.write( "in functional notation.\r\n" );
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document.write( "To draw the graph, plot the given vertex and the given\r\n" );
document.write( "point, and find some more points, say: \r\n" );
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document.write( "(-7,-5), (-4,1), (5,-5)\r\n" );
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document.write( "Now draw in the graph of the function:\r\n" );
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document.write( "Edwin
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