document.write( "Question 1044820: the minimum value of the function y=h(x) corresponds to the point (-3,2) on the x-y plane. What is the maximum value of g(x)=6-h(x+2)? \n" ); document.write( "
Algebra.Com's Answer #660254 by Edwin McCravy(20059)\"\" \"About 
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the minimum value of the function y=h(x) corresponds to the point
\n" ); document.write( "(-3,2) on the x-y plane. What is the maximum value of g(x)=6-h(x+2)?
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document.write( "Let's do it by finding specific quadratic functions for y=h(x) \r\n" );
document.write( "and y=g(x).\r\n" );
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document.write( "Let's find a quadratic function for y=h(x) that has (-3,2) as a\r\n" );
document.write( "minimum value.\r\n" );
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document.write( "h(x) = y = A(x-H)² + K which has vertex (H,K).\r\n" );
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document.write( "So choose H=-3 and K=2 and A=1, positive so it will\r\n" );
document.write( "open upward and the vertex will be at the bottom,\r\n" );
document.write( "making it a minimum, so\r\n" );
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document.write( "h(x) = (x+3)² + 2\r\n" );
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document.write( "Here is the graph of h(x)\r\n" );
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document.write( "Then \r\n" );
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document.write( "h(x+2) = (x+2+3)² + 2\r\n" );
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document.write( "h(x+2) = (x+5)² + 2\r\n" );
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document.write( "g(x) = 6-h(x+2)\r\n" );
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document.write( "g(x) = 6-[(x+5)² + 2]\r\n" );
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document.write( "g(x) = 6 - (x+5)² - 2\r\n" );
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document.write( "g(x) = -(x+5)² + 4\r\n" );
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document.write( "which has vertex (-5,4) and opens downward,\r\n" );
document.write( "because of the negative sign before (x+5)²\r\n" );
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document.write( "so its vertex (-5,4) is a maximum.\r\n" );
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document.write( "Answer: (-5,4)\r\n" );
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document.write( "Here are both graphed on the same set of axes.\r\n" );
document.write( "The red graph is of y=h(x) and the green\r\n" );
document.write( "one is y=g(x)\r\n" );
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document.write( "Edwin
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