document.write( "Question 367380: Explain how the graph of g(x)=x^2 can be transformed into the graph of h(x)=(x+5)^2+1\r
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Algebra.Com's Answer #261889 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Explain how the graph of g(x)=x^2 can be transformed into the graph of h(x)=(x+5)^2+1\r
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\n" ); document.write( "\n" ); document.write( "Can someone please explain what happened to the exponent? Lost with this
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document.write( "The exponent isn't lost.  You must be confusing (x+5) with g(x+5). But \r\n" );
document.write( "g(x+5) stands for (x+5)^2, which has the exponent 2.\r\n" );
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document.write( "Maybe the following will help you understand.\r\n" );
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document.write( "Start with the function g(x) = x^2 whose graph looks like this:\r\n" );
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document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%29\"\r\n" );
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document.write( "Replace the x in g(x) = x^2 by (x+5) which gives you:\r\n" );
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document.write( "     g(x+5) = (x+5)^2\r\n" );
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document.write( "and that shifts the graph of g(x) to the left by 5 units, to look like this:\r\n" );
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document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%2B5%29%5E2%29\"\r\n" );
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document.write( "Now let's add 1 to both sides \r\n" );
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document.write( "g(x+5) + 1  = (x+5)^2 + 1\r\n" );
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document.write( "which shifts the graph up 1 unit to look like this:\r\n" );
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document.write( "\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C%28x%2B5%29%5E2%2B1%29\"\r\n" );
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document.write( "Now all that's been done now is to give this function a brand new name, h(x)\r\n" );
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document.write( "So you can either write it\r\n" );
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document.write( "h(x) = g(x+5) + 1\r\n" );
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document.write( "or you can write it as\r\n" );
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document.write( "h(x) = (x+5)^2 + 1 \r\n" );
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document.write( "which is the final way to write it\r\n" );
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document.write( "See how these last two equations are the same, since g(x+5) stands for\r\n" );
document.write( "(h+5)^2?  Do you see that no exponent was lost? \r\n" );
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document.write( "Edwin
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