document.write( "Question 535985: Find the quadratic function that fits the data points (0,0), (6,0) and (8,2) \n" ); document.write( "

Algebra.Com's Answer #352096 by josmiceli(19441) $\"\"$ $\"About$

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$\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "(0,0)
\n" ); document.write( " $\"+0+=+a%2A0+%2B+b%2A0+%2B+c+\"$
\n" ); document.write( " $\"+c+=+0+\"$
\n" ); document.write( "(6,0)
\n" ); document.write( " $\"+0+=+a%2A6%5E2+%2B+b%2A6+%2B+0+\"$
\n" ); document.write( " $\"+36a+=+-6b+\"$
\n" ); document.write( " $\"+b+=+-6a+\"$
\n" ); document.write( "(8,2)
\n" ); document.write( " $\"+2+=+a%2A8%5E2+%2B+b%2A8+%2B+0+\"$
\n" ); document.write( " $\"+2+=+64a+%2B+8b+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+2+=+64a+%2B+8%2A%28-6a%29+\"$
\n" ); document.write( " $\"+2+=+64a+-+48a+\"$
\n" ); document.write( " $\"+16a+=+2+\"$
\n" ); document.write( " $\"+a+=+1%2F8+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+b+=+-6a+\"$
\n" ); document.write( " $\"+b+=+-3%2F4+\"$
\n" ); document.write( "The function is
\n" ); document.write( " $\"+y+=+%281%2F8%29%2Ax%5E2+-+%283%2F4%29%2Ax+\"$
\n" ); document.write( "check:
\n" ); document.write( "(8,2)
\n" ); document.write( " $\"+2+=+%281%2F8%29%2A8%5E2+-+%283%2F4%29%2A8+\"$
\n" ); document.write( " $\"+2+=+64%2F8+-+24%2F4+\"$
\n" ); document.write( " $\"+2+=+32%2F4+-+24%2F4+\"$
\n" ); document.write( " $\"+2+=+8%2F4+\"$
\n" ); document.write( " $\"+2+=+2+\"$
\n" ); document.write( "OK \n" ); document.write( "

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