document.write( "Question 167529: The graph of f (x) = ax2 + bx + c passes
\n" ); document.write( "through the points (1, k1), (2, k2), and (3, k3). Determine a,
\n" ); document.write( "b, and c for
\n" ); document.write( "(A) k1=-2, k2 = 1, k3 = 6
\n" ); document.write( "(B) k1 = 4, k2 = 3, k3=-2
\n" ); document.write( "(C) k1 = 8, k2=-5, k3 = 4\r
\n" ); document.write( "\n" ); document.write( "I attempted to solve as follows:\r
\n" ); document.write( "\n" ); document.write( "(A)-2= a + b + c
\n" ); document.write( " 1= a - b + c
\n" ); document.write( " 6= 4a + 2b +c
\n" ); document.write( "and entering this into a matrix, but it doesn't come out right.\r
\n" ); document.write( "\n" ); document.write( "What am I doing wrong?\r
\n" ); document.write( "\n" ); document.write( "Thank you!\r
\n" ); document.write( "\n" ); document.write( "Debi
\n" ); document.write( "

Algebra.Com's Answer #123477 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
The graph of \"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\" passes
\n" ); document.write( "through the points (1, k1), (2, k2), and (3, k3). Determine a,
\n" ); document.write( "b, and c for
\n" ); document.write( "
\r\n" );
document.write( "Plug \"x=1\" in:\r\n" );
document.write( "\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"\r\n" );
document.write( "\"f%281%29+=+a%281%29%5E2+%2B+b%281%29+%2B+c\"\r\n" );
document.write( "\"f%281%29+=+a%281%29+%2B+b%281%29+%2B+c\"\r\n" );
document.write( "\"f%281%29+=+a%2Bb%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "Now since the graph passes through \"matrix%281%2C5%2C%22%28%22%2C1%2C%22%2C%22%2Ck%5B1%5D%2C%22%29%22%29\"\r\n" );
document.write( "then \"f%281%29=k%5B1%5D\", so substitute \"k%5B1%5D\" for \"f%281%29\" in\r\n" );
document.write( "\r\n" );
document.write( "\"f%281%29=a%2Bb%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "or\r\n" );
document.write( "\r\n" );
document.write( "\"a%2Bb%2Bc=k%5B1%5D\"\r\n" );
document.write( "\r\n" );
document.write( "Plug \"x=2\" in:\r\n" );
document.write( "\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"\r\n" );
document.write( "\"f%282%29+=+a%282%29%5E2+%2B+b%282%29+%2B+c\"\r\n" );
document.write( "\"f%282%29+=+a%284%29+%2B+b%282%29+%2B+c\"\r\n" );
document.write( "\"f%282%29+=+4a%2B2b%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "Now since the graph passes through \"matrix%281%2C5%2C%22%28%22%2C2%2C%22%2C%22%2Ck%5B2%5D%2C%22%29%22%29\"\r\n" );
document.write( "then \"f%282%29=k%5B2%5D\", so substitute \"k%5B2%5D\" for \"f%282%29\" in\r\n" );
document.write( "\r\n" );
document.write( "\"f%282%29=4a%2B2b%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "Plug \"x=3\" in:\r\n" );
document.write( "\"f%28x%29+=+ax%5E2+%2B+bx+%2B+c\"\r\n" );
document.write( "\"f%283%29+=+a%283%29%5E2+%2B+b%283%29+%2B+c\"\r\n" );
document.write( "\"f%283%29+=+a%289%29+%2B+b%283%29+%2B+c\"\r\n" );
document.write( "\"f%283%29+=+9a%2B3b%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "Now since the graph passes through \"matrix%281%2C5%2C%22%28%22%2C3%2C%22%2C%22%2Ck%5B3%5D%2C%22%29%22%29\"\r\n" );
document.write( "then \"f%283%29=k%5B3%5D\", so substitute \"k%5B3%5D\" for \"f%283%29\" in\r\n" );
document.write( "\r\n" );
document.write( "\"f%283%29+=+9a%2B3b%2Bc\"\r\n" );
document.write( "\r\n" );
document.write( "\"k%5B3%5D+=+9a%2B3b%2Bc\" or\r\n" );
document.write( "\r\n" );
document.write( "\"9a%2B3b%2Bc=k%5B3%5D\"\r\n" );
document.write( "\r\n" );
document.write( "So we have this system:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=k%5B1%5D%2C+4a%2B2b%2Bc=k%5B2%5D%2C+9a%2B3b%2Bc=k%5B3%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------------------\r\n" );
document.write( "(A) \"matrix%281%2C5%2Ck1=-2%2C%22%2C%22%2Ck2+=+1%2C%22%2C%22%2Ck3+=+6%29\"\r\n" );
document.write( "\r\n" );
document.write( "the system\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=k%5B1%5D%2C+4a%2B2b%2Bc=k%5B2%5D%2C+9a%2B3b%2Bc=k%5B3%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "becomes\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=-2%2C+4a%2B2b%2Bc=1%2C+9a%2B3b%2Bc=6%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve this system and get \"matrix%281%2C5%2C+a=1%2C%22%2C%22%2C+b=0%2C+%22%2C%22%2C+c=-3%29\"\r\n" );
document.write( "\r\n" );
document.write( "--------\r\n" );
document.write( "\r\n" );
document.write( "(B) \"matrix%281%2C5%2Ck1=4%2C%22%2C%22%2Ck2+=+3%2C%22%2C%22%2Ck3+=+-2%29\"\r\n" );
document.write( "\r\n" );
document.write( "the system\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=k%5B1%5D%2C+4a%2B2b%2Bc=k%5B2%5D%2C+9a%2B3b%2Bc=k%5B3%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "becomes\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=4%2C+4a%2B2b%2Bc=3%2C+9a%2B3b%2Bc=-2%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve this system and get \"matrix%281%2C5%2C+a=-2%2C%22%2C%22%2C+b=5%2C+%22%2C%22%2C+c=1%29\"\r\n" );
document.write( "\r\n" );
document.write( "----------\r\n" );
document.write( "\r\n" );
document.write( "(C) \"matrix%281%2C5%2Ck1=8%2C%22%2C%22%2Ck2+=+-5%2C%22%2C%22%2Ck3+=+4%29\"\r\n" );
document.write( "\r\n" );
document.write( "the system\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=k%5B1%5D%2C+4a%2B2b%2Bc=k%5B2%5D%2C+9a%2B3b%2Bc=k%5B3%5D%29\"\r\n" );
document.write( "\r\n" );
document.write( "becomes\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%2Bb%2Bc=8%2C+4a%2B2b%2Bc=-5%2C+9a%2B3b%2Bc=4%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve this system and get \"matrix%281%2C5%2C+a=11%2C%22%2C%22%2C+b=-46%2C+%22%2C%22%2C+c=43%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );