document.write( "Question 813287: Find an equation in standard form of the parabola passing through the points.
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Algebra.Com's Answer #489592 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "y = a(x - h)² + k\r\n" );
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document.write( "Substitute (x,y) = (1,-1)\r\n" );
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document.write( "-1 = a(1 - h)² + k\r\n" );
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document.write( "Substitute (x,y) = (2,-1)\r\n" );
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document.write( "-5 = a(2 - h)² + k\r\n" );
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document.write( "Substitute (x,y) = (3,-7)\r\n" );
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document.write( "-7 = a(3 - h)² + k\r\n" );
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document.write( "Solve this system:\r\n" );
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document.write( "-1 = a(1 - h)² + k\r\n" );
document.write( "-5 = a(2 - h)² + k\r\n" );
document.write( "-7 = a(3 - h)² + k\r\n" );
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document.write( "Solve the first for k\r\n" );
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document.write( "            -1 = a(1 - h)² + k\r\n" );
document.write( "-1 - a(1 - h)² = k\r\n" );
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document.write( "Substitute in the second and simplify\r\n" );
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document.write( "-5 = a(2 - h)² + k\r\n" );
document.write( "-5 = a(2 - h)² - 1 - a(1 - h)²\r\n" );
document.write( "-4 = a(2 - h)² - a(1 - h)²\r\n" );
document.write( "-4 = a[(2-h)² - (1-h)²]\r\n" );
document.write( "-4 = a[(2-h) - (1-h)][(2-h) + (1-h)]\r\n" );
document.write( "-4 = a[2 - h - 1 + h][2 - h + 1 - h]\r\n" );
document.write( "-4 = a[1][3 - 2h]\r\n" );
document.write( "-4 = a(3 - 2h)\r\n" );
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document.write( "Substitute in the thirdd and simplify\r\n" );
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document.write( "-7 = a(3 - h)² + k\r\n" );
document.write( "-7 = a(3 - h)² - 1 - a(1 - h)²\r\n" );
document.write( "-6 = a(3 - h)² - a(1 - h)²\r\n" );
document.write( "-6 = a[(3-h)² - (1-h)²]\r\n" );
document.write( "-6 = a[(3-h) - (1-h)][(3-h) + (1-h)]\r\n" );
document.write( "-6 = a[3 - h - 1 + h][3 - h + 1 - h]\r\n" );
document.write( "-6 = a[2][4 - 2h]\r\n" );
document.write( "-6 = 2a(4 - 2h)\r\n" );
document.write( "-6 = 2a·2(2 - h)\r\n" );
document.write( "-6 = 4a(2 - h)\r\n" );
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document.write( "Divide equals by equals:\r\n" );
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document.write( "\"%28-4%29%2F%28-6%29\"\"%22%22=%22%22\"\"%28a%283+-+2h%29%29%2F%284a%282-h%29%29\"\r\n" );
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document.write( "\"2%2F3\"\"%22%22=%22%22\"\"%28cross%28a%29%283+-+2h%29%29%2F%284cross%28a%29%282-h%29%29\"\r\n" );
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document.write( "\"2%2F3\"\"%22%22=%22%22\"\"%283+-+2h%29%2F%284%282-h%29%29\"\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "8(2-h) = 3(3-2h)\r\n" );
document.write( "16-8h = 9-6h\r\n" );
document.write( "-2h = -7\r\n" );
document.write( "  h = \"7%2F2\"\r\n" );
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document.write( "Sustitute in\r\n" );
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document.write( "-1 = a(1 - h)² + k\r\n" );
document.write( "-5 = a(2 - h)² + k\r\n" );
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document.write( "-1 = a(1 - \"7%2F2\")² + k\r\n" );
document.write( "-5 = a(2 - \"7%2F2\")² + k\r\n" );
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document.write( "-1 = a\"%28-5%2F2%29%5E2%7D%7C%7D+%2B+k%0D%0A-5+=+a%7B%7B%7B%28-3%2F2%29%5E2\" + k\r\n" );
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document.write( "-1 = a\"%2825%2F4%29%7D%7C%7D+%2B+k%0D%0A-5+=+a%7B%7B%7B%289%2F4%29\" + k\r\n" );
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document.write( "Multiply both equations through by 4\r\n" );
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document.write( " -4 = 25a + 4k\r\n" );
document.write( "-20 =  9a + 4k\r\n" );
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document.write( "Multiply the 1st eq. by -1 and add term by term\r\n" );
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document.write( "  4 = -25a - 4k \r\n" );
document.write( "-20 =   9a + 4k\r\n" );
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document.write( "-16 = -16a\r\n" );
document.write( "  1 = a\r\n" );
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document.write( "Substitute in  \r\n" );
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document.write( "-4 = 25a + 4k\r\n" );
document.write( "-4 = 25(1) + 4k\r\n" );
document.write( "-4 = 25 + 4k\r\n" );
document.write( "-29 = 4k\r\n" );
document.write( "\"-29%2F4\" = k\r\n" );
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document.write( "So the equation of the parabola in standard form is\r\n" );
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document.write( "y = a(x - h)² + k\r\n" );
document.write( "y = 1(x - \"7%2F2\")²  - \"29%2F4\"\r\n" );
document.write( "y = (x - \"7%2F2\")²  - \"29%2F4\"\r\n" );
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document.write( "Edwin
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