document.write( "Question 441899: Find the values of a,b,and c such that the parabola y=ax^2+bx+c contains the points (-3,3),(-1,5)and (3,33). \n" ); document.write( "

Algebra.Com's Answer #304881 by Gogonati(855) $\"\"$ $\"About$

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Plugging the coordinates of the points into $\"y=ax%5E2%2Bbx%2Bc\"$ , we get the system:\r
\n" ); document.write( "\n" ); document.write( " $\"system%283=9a-3b%2Bc%2C+-1=25a%2B5b%2Bc%2C+33=9a%2B3b%2Bc%29\"$ . Subtracting first equation from \r
\n" ); document.write( "\n" ); document.write( "the third we get: $\"30=6b\"$ => $\"b=5\"$ .Isolate c from the first and second \r
\n" ); document.write( "\n" ); document.write( "equation:c=3-9a+3b and c=-1-25a-5b, from these two equalities we get:\r
\n" ); document.write( "\n" ); document.write( "3-9a+3b=-1-25a-5b simplifying this equality we get:4a+2b=-1, substituting b=5,\r
\n" ); document.write( "\n" ); document.write( "we have: 4a+2*5=-1 => a=-11/4. Substituting a and b we find c:\r
\n" ); document.write( "\n" ); document.write( "c=3+99/4+15 => c=171/4.\r
\n" ); document.write( "\n" ); document.write( "You can solve the system using Cramer's Rule.\r
\n" ); document.write( "\n" ); document.write( "Done.\r
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