document.write( "Question 980271: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,-2), (-2, 19) and (3,4). use the Guassian elimination \n" ); document.write( "

Algebra.Com's Answer #601488 by Fombitz(32388) $\"\"$ $\"About$

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(1,-2): $\"-2=a%281%29%5E2%2Bb%281%29%2Bc\"$
\n" ); document.write( "1. $\"a%2Bb%2Bc=-2\"$
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\n" ); document.write( "(-2,19): $\"-2=a%28-2%29%5E2%2Bb%28-2%29%2Bc\"$
\n" ); document.write( "2. $\"4a-2b%2Bc=19\"$
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\n" ); document.write( "(3,4) : $\"4=a%283%29%5E2%2Bb%283%29%2Bc\"$
\n" ); document.write( "3. $\"9a%2B3b%2Bc=4\"$
\n" ); document.write( "Subtract the first equation from second and third.
\n" ); document.write( " $\"4a-2b%2Bc-a-b-c=19-%28-2%29\"$
\n" ); document.write( " $\"3a-3b=21\"$
\n" ); document.write( "4. $\"a-b=7\"$
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\n" ); document.write( " $\"9a%2B3b%2Bc-a-b-c=4-%282%29\"$
\n" ); document.write( " $\"8a%2B2b=6\"$
\n" ); document.write( "5. $\"4a%2Bb=3\"$
\n" ); document.write( "Now add eq. 4 and eq. 5,
\n" ); document.write( " $\"a-b%2B4a%2Bb=7%2B3\"$
\n" ); document.write( " $\"5a=10\"$
\n" ); document.write( " $\"a=2\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"2-b=7\"$
\n" ); document.write( " $\"-b=5\"$
\n" ); document.write( " $\"b=-5\"$
\n" ); document.write( "and,
\n" ); document.write( " $\"2-5%2Bc=-2\"$
\n" ); document.write( " $\"c=1\"$
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\n" ); document.write( " $\"y=2x%5E2-5x%2B1\"$ \r
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