document.write( "Question 942047: Find the equation of the parabola with axis parallel to 0x and passing through (5,4),(11,-2),(21,-4). \n" ); document.write( "
Algebra.Com's Answer #574331 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
So the general equation would be,
\n" ); document.write( "\"x=ay%5E2%2Bby%2Bc\"
\n" ); document.write( "\"5=16a%2B4b%2Bc\"
\n" ); document.write( "\"11=4a-2b%2Bc\"
\n" ); document.write( "\"21=16a-4b%2Bc\"
\n" ); document.write( "Use Cramer's rule to solve for \"a\",\"b\",\"c\".
\n" ); document.write( "\"A=%28matrix%283%2C3%2C16%2C4%2C1%2C4%2C-2%2C1%2C16%2C-4%2C1%29%29\"
\n" ); document.write( "\"abs%28A%29=96\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "\"A%5Ba%5D=%28matrix%283%2C3%2C5%2C4%2C1%2C11%2C-2%2C1%2C21%2C-4%2C1%29%29\"
\n" ); document.write( "\"abs%28A%5Ba%5D%29=48\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "\"A%5Bb%5D=%28matrix%283%2C3%2C16%2C5%2C1%2C4%2C11%2C1%2C16%2C21%2C1%29%29\"
\n" ); document.write( "\"abs%28A%5Bb%5D%29=-192\"
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( "\"A%5Bc%5D=%28matrix%283%2C3%2C16%2C4%2C5%2C4%2C-2%2C11%2C16%2C-4%2C21%29%29\"
\n" ); document.write( "\"abs%28A%5Bc%5D%29=480\"
\n" ); document.write( "So then,
\n" ); document.write( "\"a=abs%28A%5Ba%5D%29%2Fabs%28A%29=%2848%29%2F96=1%2F2\"
\n" ); document.write( "\"b=abs%28A%5Bb%5D%29%2Fabs%28A%29=%28-192%29%2F96=-2\"
\n" ); document.write( "\"c=abs%28A%5Bc%5D%29%2Fabs%28A%29=%28480%29%2F96=5\"
\n" ); document.write( "So,
\n" ); document.write( "\"x=%281%2F2%29y%5E2-2y%2B5\"
\n" ); document.write( "
\n" ); document.write( "
\n" );