document.write( "Question 661828: Write the equation if the quadratic function with roots -9 and a vertex at -6, -1 \n" ); document.write( "
Algebra.Com's Answer #411821 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Since -9 is a root, it has an x-intercept of (-9,0) \r\n" );
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document.write( "We plot those given points:\r\n" );
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document.write( "We know that the axis of symmetry is a vertical line through\r\n" );
document.write( "the vertex:\r\n" );
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document.write( "that goes through the vertex.  So we draw that:\r\n" );
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document.write( "And we can sketch in the parabola so that the green line\r\n" );
document.write( "bisects it:\r\n" );
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document.write( "All quadratic functions have the equation\r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "where the vertex is (h,k).  In this case (h,k) = (-6,-1), so the\r\n" );
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document.write( "equation is\r\n" );
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document.write( "y = a(x - (-6))² + (-1), or upon simplifying,\r\n" );
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document.write( "y = a(x + 6)² - 1\r\n" );
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document.write( "We only need the value of a.\r\n" );
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document.write( "It goes through (-9,0) so we substitute x=-9 and y=0\r\n" );
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document.write( "y = a(x + 6)² - 1\r\n" );
document.write( "0 = a(-9 + 6)² - 1\r\n" );
document.write( "0 = a(-3)² - 1\r\n" );
document.write( "0 = a(9) - 1\r\n" );
document.write( "0 = 9a - 1\r\n" );
document.write( "1 = 9a\r\n" );
document.write( "\"1%2F9\" = a\r\n" );
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document.write( "So the equation is\r\n" );
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document.write( "y = \"1%2F9\"(x + 6)² - 1\r\n" );
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document.write( "You can leave it like that or you can continue:\r\n" );
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document.write( "y = \"1%2F9\"(x + 6)(x + 6) - 1\r\n" );
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document.write( "y = \"1%2F9\"(x² + 12x + 36) - 1\r\n" );
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document.write( "y = \"1%2F9\"(x² + 12x + 36) - \"9%2F9\"\r\n" );
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document.write( "y = \"%28x%5E2+%2B+12x+%2B+36%29%2F9\" - \"9%2F9\"\r\n" );
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document.write( "y = \"%28x%5E2+%2B+12x+%2B+36+-+9%29%2F9\"\r\n" );
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document.write( "y = \"%28x%5E2+%2B+12x+%2B+27%29%2F9\"\r\n" );
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document.write( "From there you can either factor the numerator\r\n" );
document.write( "and leave it like this:\r\n" );
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document.write( "y = \"%28%28x%2B3%29%28x%2B9%29%29%2F9\"\r\n" );
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document.write( "Or you can take this:\r\n" );
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document.write( "y = \"%28x%5E2+%2B+12x+%2B+27%29%2F9\"\r\n" );
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document.write( "write it as\r\n" );
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document.write( "y = \"x%5E2%2F9\" + \"12%2F9\"x + \"27%2F9\"\r\n" );
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document.write( "and then as\r\n" );
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document.write( "y = \"1%2F9\"x² + \"4%2F3\"x + 3\r\n" );
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document.write( "Edwin
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