document.write( "Question 909255: write an equation for a quadratic given the following:\r
\n" ); document.write( "\n" ); document.write( "x-intercepts are (2,0) and (5,0) and y-intercept is (0,6)\r
\n" ); document.write( "\n" ); document.write( "I know that it means I have (x-2) and (x-5) for my equation. I multiplied them to get x^2 - 7x + 35. I'm not sure how to incorporate the y-intercept.\r
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\n" ); document.write( "6= x^2 - 7x + 35\r
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Algebra.Com's Answer #551734 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor gave you a way that will work ONLY if you are given \r\n" );
document.write( "the intercepts.  But you should do it a more general way, because \r\n" );
document.write( "the three points you are given will not always be intercepts.  For \r\n" );
document.write( "instance you may be given the points (7,6), (-3,24) and (12,42).  \r\n" );
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document.write( "Here's what you should do instead.  You must start with\r\n" );
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document.write( "y = ax˛ + bx + c\r\n" );
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document.write( "Then you substitute in each of the three points, the x-coordinate\r\n" );
document.write( "for x, and the y-coordinate for y.\r\n" );
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document.write( "Substituting (2,0)\r\n" );
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document.write( "y = ax˛ + bx + c\r\n" );
document.write( "0 = a(2)˛ + b(2) + c\r\n" );
document.write( "0 = 4a + 2b + c\r\n" );
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document.write( "Substituting (5,0)\r\n" );
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document.write( "y = ax˛ + bx + c\r\n" );
document.write( "0 = a(5)˛ + b(5) + c\r\n" );
document.write( "0 = 25a + 5b + c\r\n" );
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document.write( "Substituting (0,6)\r\n" );
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document.write( "y = ax˛ + bx + c\r\n" );
document.write( "6 = a(0)˛ + b(0) + c\r\n" );
document.write( "6 = 0 + 0 + c\r\n" );
document.write( "6 = c\r\n" );
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document.write( "Now you have three equations:\r\n" );
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document.write( "0 =  4a + 2b + c\r\n" );
document.write( "0 = 25a + 5b + c\r\n" );
document.write( "6 = c\r\n" );
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document.write( "Substitute 6 for c in the first two:\r\n" );
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document.write( "0 =  4a + 2b + 6\r\n" );
document.write( "0 = 25a + 5b + 6\r\n" );
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document.write( "Eliminate the b's by multiplying the first equation by -5\r\n" );
document.write( "and the second equation by 2\r\n" );
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document.write( "0 = -20a - 10b - 30\r\n" );
document.write( "0 =  50a + 10b + 12\r\n" );
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document.write( "0 =  30a       - 18\r\n" );
document.write( "18 = 30a\r\n" );
document.write( "\"18%2F30\" = a\r\n" );
document.write( "\"3%2F5\" = a\r\n" );
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document.write( "Substitute \"3%2F5\" for a in\r\n" );
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document.write( "  0 = 25a + 5b + 6\r\n" );
document.write( "  0 = 25\"%283%2F5%29\" + 5b + 6\r\n" );
document.write( "  0 = 15 + 5b + 6\r\n" );
document.write( "  0 = 21 + 5b\r\n" );
document.write( "-21 = 5b\r\n" );
document.write( "\"-21%2F5\" = b\r\n" );
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document.write( "Now substitute \"3%2F5\" for a, \"-21%2F5\" = b, and 6 for c in\r\n" );
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document.write( "y = ax˛ + bx + c\r\n" );
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document.write( "and get:\r\n" );
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document.write( "\"y=expr%283%2F5%29x%5E2-expr%2821%2F5%29x%2B6\"\r\n" );
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document.write( "This method will always work whether the points given happen to be\r\n" );
document.write( "intercepts or not.\r\n" );
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document.write( "Edwin
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