document.write( "Question 953081: Find the quadratic function that includes each set of values.\r
\n" ); document.write( "\n" ); document.write( "(1, 0), (2, 5), (4, 21) \n" ); document.write( "

Algebra.Com's Answer #582018 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
the general form is:
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "( 1,0 )
\n" ); document.write( " $\"+0+=+a%2A1%5E2+%2B+b%2A1+%2B+c+\"$
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+0+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "( 2,5 )
\n" ); document.write( " $\"+5+=+a%2A2%5E2+%2B+b%2A2+%2B+c+\"$
\n" ); document.write( "(2) $\"+4a+%2B+2b+%2B+c+=+5+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "( 4,21 )
\n" ); document.write( " $\"+21+=+a%2A4%5E2+%2B+b%2A4+%2B+c+\"$
\n" ); document.write( "(3) $\"+16a+%2B+4b+%2B+c+=+21+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+4a+%2B+2b+%2B+c+=+5+\"$
\n" ); document.write( "(1) $\"+-a+-+b+-+c+=+0+\"$
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"+3a+%2B+b+=+5+\"$
\n" ); document.write( "Multiply both sides by $\"+4+\"$
\n" ); document.write( "and subtract this result from (3)
\n" ); document.write( " $\"+16a+%2B+4b+%2B+c+=+21+\"$
\n" ); document.write( " $\"+-12a+-+4b+=+-20+\"$
\n" ); document.write( "----------------------
\n" ); document.write( " $\"+4a+%2B+c+=+1+\"$
\n" ); document.write( " $\"+c+=+-4a+%2B+1+\"$
\n" ); document.write( "Plug this into (1)
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+-4a+%2B+1+=+0+\"$
\n" ); document.write( "also, from above:
\n" ); document.write( " $\"+3a+%2B+b+=+5+\"$
\n" ); document.write( " $\"+b+=+-3a+%2B+5+\"$
\n" ); document.write( "Plug this into (1)
\n" ); document.write( "(1) $\"+a+%2B+-3a+%2B+5+%2B+-4a+%2B+1+=+0+\"$
\n" ); document.write( "(1) $\"+-6a++=+-6+\"$
\n" ); document.write( "(1) $\"+a+=+1+\"$
\n" ); document.write( "----------------
\n" ); document.write( " $\"+c+=+-4a+%2B+1+\"$
\n" ); document.write( " $\"+c+=+-4%2A1+%2B+1+\"$
\n" ); document.write( " $\"+c+=+-3+\"$
\n" ); document.write( "--------------
\n" ); document.write( " $\"+b+=+-3a+%2B+5+\"$
\n" ); document.write( " $\"+b+=+-3%2A1+%2B+5+\"$
\n" ); document.write( " $\"+b+=+2+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Plug these results into:
\n" ); document.write( " $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( " $\"+y+=+x%5E2+%2B+2x+-+3+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "check:
\n" ); document.write( "( 4,21 )
\n" ); document.write( " $\"+21+=+4%5E2+%2B+2%2A4+-+3+\"$
\n" ); document.write( " $\"+21+=+16+%2B+8+-+3+\"$
\n" ); document.write( " $\"+21+=+21+\"$
\n" ); document.write( "You can check the other 2 points\r
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