document.write( "Question 75529: what quadractic function represents a porabola whose vertex is at (6,1) and passes through (4,9) \n" ); document.write( "
Algebra.Com's Answer #54253 by Edwin McCravy(20086)\"\" \"About 
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document.write( "what quadractic function represents a \r\n" );
document.write( "parabola whose vertex is at (6,1) and \r\n" );
document.write( "passes through (4,9)\r\n" );
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document.write( "Any quadratic function can be expressed as\r\n" );
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document.write( "f(x) = a(x - h)² + k\r\n" );
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document.write( "where (h,k) is the vertex\r\n" );
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document.write( "So since (h,k) = (6,1),\r\n" );
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document.write( "f(x) = a(x - 6)² + 1\r\n" );
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document.write( "Since it passes through (4,9)\r\n" );
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document.write( "f(4) = 9\r\n" );
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document.write( "and also\r\n" );
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document.write( "f(4) = a(4 - 6)² + 1 \r\n" );
document.write( "     = a(-2)² + 1 \r\n" );
document.write( "     = a(4) + 1\r\n" );
document.write( "     = 4a + 1\r\n" );
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document.write( "Since both 9 and 4a + 1\r\n" );
document.write( "equal to f(4), we can\r\n" );
document.write( "set them equal to each other:\r\n" );
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document.write( "9 = 4a + 1\r\n" );
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document.write( "Solve that and get a = 2\r\n" );
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document.write( "So substitute 2 for a in\r\n" );
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document.write( "f(x) = a(x - 6)² + 1\r\n" );
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document.write( "f(x) = 2(x - 6)² + 1\r\n" );
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document.write( "or if you like you can multiply\r\n" );
document.write( "that out and simplify:\r\n" );
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document.write( "f(x) = 2(x - 6)(x - 6) + 1\r\n" );
document.write( "     = 2(x² - 6x - 6x + 36) + 1\r\n" );
document.write( "     = 2(x² - 12x + 36) + 1\r\n" );
document.write( "     = 2x² - 24x + 72 + 1\r\n" );
document.write( "     = 2x² - 24x + 73\r\n" );
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document.write( "Edwin
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