document.write( "Question 540835: Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4) \n" ); document.write( "
Algebra.Com's Answer #353889 by AnlytcPhil(1806)\"\" \"About 
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Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4)
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document.write( "It has the form\r\n" );
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document.write( "f(x) = a(x - h)² + k where the vertex is (h,k),\r\n" );
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document.write( "Since we are given that the vertex is (1,8), we have\r\n" );
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document.write( "f(x) = a(x - 1)² + 8\r\n" );
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document.write( "Since the parabola passes through the point (x,y) = (-3,4), we will\r\n" );
document.write( "substitute -3 for x and since y = f(x) we will substitute 4 for f(x):\r\n" );
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document.write( "4 = a(-3 - 1)² + 8\r\n" );
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document.write( "4 = a(-4)² + 8\r\n" );
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document.write( "4 = a(16) + 8\r\n" );
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document.write( "4 = 16a + 8\r\n" );
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document.write( "-4 = 16a\r\n" );
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document.write( "\"%28-4%29%2F16\" = a\r\n" );
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document.write( "\"-1%2F4\" = a\r\n" );
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document.write( "We substitute \"-1%2F4\" for a in\r\n" );
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document.write( "f(x) = a(x - 1)² + 8\r\n" );
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document.write( "f(x) = \"-1%2F4\"(x - 1)² + 8\r\n" );
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document.write( "That is in vertex form.  To get it in standard form  f(x) = ax² + bx + c\r\n" );
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document.write( "f(x) = \"-1%2F4\"(x - 1)(x - 1) + 8\r\n" );
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document.write( "f(x) = \"-1%2F4\"(x² - 2x + 1) + 8\r\n" );
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document.write( "f(x) = \"-1%2F4\"x² - \"-1%2F4\"·2x + \"-1%2F4\"·1 + 8\r\n" );
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document.write( "f(x) = \"-1%2F4\"x² + \"1%2F2\"x - \"1%2F4\" + 8\r\n" );
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document.write( "f(x) = \"-1%2F4\"x² + \"1%2F2\"x - \"1%2F4\" + 32/4\r\n" );
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document.write( "f(x) = \"-1%2F4\"x² + \"1%2F2\"x + \"31%2F4\"\r\n" );
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document.write( "Edwin
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