document.write( "Question 1147599: Find the equation of the parabola whose axis is parallel to the x-axis and passes through the points (3, 1), (0, 0), and (8,-4) \n" ); document.write( "
Algebra.Com's Answer #768996 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Parabolas like this have standard equation:\r\n" );
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document.write( "\"%28y-k%5E%22%22%29%5E2=4p%28x-h%5E%22%22%29\"\r\n" );
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document.write( "Substitute (x,y) = (0,0):\r\n" );
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document.write( "\"%280-k%29%5E2=4p%280-h%29\"\r\n" );
document.write( "\"k%5E2=4p%28-h%29\"\r\n" );
document.write( "\"k%5E2=-4ph\"\r\n" );
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document.write( "\"%28y-k%5E%22%22%29%5E2=4p%28x-h%5E%22%22%29\"\r\n" );
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document.write( "Substitute (x,y) = (3,1):\r\n" );
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document.write( "\"%281-k%29%5E2=4p%283-h%29\"\r\n" );
document.write( "\"1-2k%2Bk%5E2=12p-4ph%29\"\r\n" );
document.write( "Substitute +k² for -4ph\r\n" );
document.write( "\"1-2k%2Bk%5E2=12p%2Bk%5E2%29\"\r\n" );
document.write( "\"1-2k=12p\"\r\n" );
document.write( "\"12p%2B2k=1\"\r\n" );
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document.write( "Substitute (x,y) = (8,-4):\r\n" );
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document.write( "\"%28-4-k%29%5E2=4p%288-h%29\"\r\n" );
document.write( "\"16%2B8k%2Bk%5E2=32p-4ph%29\"\r\n" );
document.write( "Substitute +k² for -4ph\r\n" );
document.write( "\"16%2B8k%2Bk%5E2=32p%2Bk%5E2%29\"\r\n" );
document.write( "\"16%2B8k=32p\"\r\n" );
document.write( "\"32p-8k=16\"\r\n" );
document.write( "That can be divided through by 8\r\n" );
document.write( "\"4p-k=2\"\r\n" );
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document.write( "Solve this system:\r\n" );
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document.write( "\"system%2812p%2B2k=1%2C4p-k=2%29\"\r\n" );
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document.write( "And you'll get p=1/4, k=-1\r\n" );
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document.write( "Substitute in \"k%5E2=-4ph\"\r\n" );
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document.write( "\"%28-1%29%5E2=-4%281%2F4%29h\"\r\n" );
document.write( "\"1=-h\"\r\n" );
document.write( "\"h=-1\"\r\n" );
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document.write( "So substitute for h,k, and p:\r\n" );
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document.write( "\"%28y-%28-1%29%5E%22%22%29%5E2=4%281%2F4%29%28x-%28-1%29%5E%22%22%29\"\r\n" );
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document.write( "\"%28y%2B1%5E%22%22%29%5E2=%281%29%28x%2B1%5E%22%22%29\"\r\n" );
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document.write( "\"%28y%2B1%5E%22%22%29%5E2=x%2B1%5E%22%22\"    <---answer\r\n" );
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document.write( "Edwin
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