document.write( "Question 1091208: Given the graph with the points: (1,-2)(5,0)(10,1),write the radical function for f(x) \n" ); document.write( "
Algebra.Com's Answer #705610 by MathLover1(20849)\"\" \"About 
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the radical function would be:\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\"\r
\n" ); document.write( "\n" ); document.write( "use the points
\n" ); document.write( "(\"1\",\"-2\"),
\n" ); document.write( " (\"5\",\"0\"),
\n" ); document.write( "(\"10\",\"1\") to find \"a\",\"b\", and \"c\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\"...........(\"1\",\"-2\")\r
\n" ); document.write( "\n" ); document.write( "\"-2=a%2Asqrt%281-b%29%2Bc\"....solve for \"c\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"c=-2-a%2Asqrt%281-b%29\".......eq.1\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\"..........(\"5\",\"0\")
\n" ); document.write( "\"0=a%2Asqrt%285-b%29%2Bc\"..........solve for \"c\"
\n" ); document.write( "\"c=-a%2Asqrt%285-b%29\".......eq.2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\"..........(\"10\",\"1\")
\n" ); document.write( "\"1=a%2Asqrt%2810-b%29%2Bc\"..........solve for \"c\"\r
\n" ); document.write( "\n" ); document.write( "\"c=1-a%2Asqrt%2810-b%29\".......eq.3\r
\n" ); document.write( "\n" ); document.write( "from eq.1 and eq.2 we have:\r
\n" ); document.write( "\n" ); document.write( "\"-2-a%2Asqrt%281-b%29=-a%2Asqrt%285-b%29\".....both sides multiply by \"-1\"\r
\n" ); document.write( "\n" ); document.write( "\"2%2Ba%2Asqrt%281-b%29=a%2Asqrt%285-b%29\"............square both sides\r
\n" ); document.write( "\n" ); document.write( "\"%282%2Ba%2Asqrt%281-b%29%29%5E2=%28a%2Asqrt%285-b%29%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "\"4%2B2a%2Asqrt%281-b%29%2Ba%5E2%281-b%29=a%5E2%285-b%29\"\r
\n" ); document.write( "\n" ); document.write( "\"2a%2Asqrt%281-b%29=a%5E2%285-b%29-a%5E2%281-b%29-4\"
\n" ); document.write( "\"2a%2Asqrt%281-b%29=5a%5E2-a%5E2b-a%5E2%2Ba%5E2b-4\"
\n" ); document.write( "\"2a%2Asqrt%281-b%29=4a%5E2-4\"
\n" ); document.write( "\"sqrt%281-b%29=4a%5E2%2F2a-4%2F2a\"
\n" ); document.write( "\"sqrt%281-b%29=2a-2%2Fa\"
\n" ); document.write( "\"sqrt%281+-+b%29+=+%282+%28a+-+1%29+%28a+%2B+1%29%29%2Fa\".......square both sides
\n" ); document.write( "\"1+-+b+=+%28%282+%28a+-+1%29+%28a+%2B+1%29%29%2Fa%29%5E2\"....solve for \"b\"
\n" ); document.write( "\"b=1+-+%284+%28a+-+1%29%5E2+%28a+%2B+1%29%5E2%29%2Fa%5E2\"..............eq.b\r
\n" ); document.write( "\n" ); document.write( "from eq.2 and eq.3 we have:\r
\n" ); document.write( "\n" ); document.write( "\"1-a%2Asqrt%2810-b%29=-a%2Asqrt%285-b%29\"
\n" ); document.write( "\"1-asqrt%2810-b%29%2Basqrt%285-b%29=0\"\r
\n" ); document.write( "\n" ); document.write( "\"1%2Ba%28sqrt%285-b%29-sqrt%2810-b%29%29=0\"..........solve for \"b\"\r
\n" ); document.write( "\n" ); document.write( "\"b+=+%28-25+a%5E4+%2B+30+a%5E2+-+1%29%2F%284+a%5E2%29\"...........eq.b1\r
\n" ); document.write( "\n" ); document.write( "from .eq.b and .eq.b1:\r
\n" ); document.write( "\n" ); document.write( " ......solve for \"a\"\r
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "to make it short, you will have
\n" ); document.write( "\"highlight%28a=1%29\" or \"highlight%28a=-1%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to \"b=1+-+%284+%28a+-+1%29%5E2+%28a+%2B+1%29%5E2%29%2Fa%5E2\"..............eq.b, plug in \"a=1\" \r
\n" ); document.write( "\n" ); document.write( "\"b=1+-+%284+%281+-+1%29%5E2+%281%2B+1%29%5E2%29%2F1%5E2\"
\n" ); document.write( "\"b=1+-+%284+%2A0+%2A4%29%2F1\"
\n" ); document.write( "\"highlight%28b=1+%29\"\r
\n" ); document.write( "\n" ); document.write( "\"b=1+-+%284+%28a+-+1%29%5E2+%28a+%2B+1%29%5E2%29%2Fa%5E2\"..............eq.b, plug in \"a=-1\" \r
\n" ); document.write( "\n" ); document.write( "\"b=1+-+%284+%28-1+-+1%29%5E2+%28-1%2B+1%29%5E2%29%2F%28-1%29%5E2\"
\n" ); document.write( "\"b=1+-+%284+%2A4+%2A0%29%2F1\"
\n" ); document.write( "\"highlight%28b=1+%29\"; so, there is one double solution for \"b\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find \"c\":\r
\n" ); document.write( "\n" ); document.write( "\"c=-a%2Asqrt%285-b%29\".......eq.2...............\"highlight%28b=1%29\" and \"highlight%28a=1%29\"
\n" ); document.write( "\"c=-1%2Asqrt%285-1%29\"
\n" ); document.write( "\"c=-sqrt%284%29\"
\n" ); document.write( "\"highlight%28c=-2%29\" \r
\n" ); document.write( "\n" ); document.write( "\"c=-a%2Asqrt%285-b%29\".......eq.2...............\"highlight%28b=1%29\" and \"highlight%28a=-1%29\"
\n" ); document.write( "\"c=-%28-1%29%2Asqrt%285-1%29\"
\n" ); document.write( "\"c=1sqrt%284%29\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28c=2%29\" \r
\n" ); document.write( "\n" ); document.write( "your solutions are:\r
\n" ); document.write( "\n" ); document.write( "\"a=1\" , \"b=1\", \"c=-2\" or\r
\n" ); document.write( "\n" ); document.write( "\"a=-1\" , \"b=1\", \"c=2\" \r
\n" ); document.write( "\n" ); document.write( "the radical function would be:\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\" .....if \"a=1\" , \"b=1\", \"c=-2\"
\n" ); document.write( "\"highlight%28f%28x%29=sqrt%28x-1%29-2%29\"\r
\n" ); document.write( "\n" ); document.write( "or
\n" ); document.write( "\"f%28x%29=a%2Asqrt%28x-b%29%2Bc\" .....if \"a=-1\" , \"b=1\", \"c=2\"
\n" ); document.write( "\"f%28x%29=-sqrt%28x-1%29%2B2\"->
\n" ); document.write( "since given point (\"1\",\"-2\"), the value of \"x=1\" will give us \"sqrt%281-1%29=sqrt%280%29\" and \"y=2\"
\n" ); document.write( "so, disregard \"f%28x%29=-sqrt%28x-1%29%2B2\"\r
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