document.write( "Question 766776: Derive a quadratic equation using the following points: (1, -4), (2, -5), (3, -10) \n" ); document.write( "

Algebra.Com's Answer #467257 by tommyt3rd(5050) $\"\"$ $\"About$

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y = ax^2+bx+c\r
\n" ); document.write( "\n" ); document.write( "(1) (1, -4) -> -4=a+b+c ,
\n" ); document.write( "(2) (2, -5) -> -5= 4a+2b+c,
\n" ); document.write( "(3) (3, -10) -> -10=9a+3b+c\r
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\n" ); document.write( "\n" ); document.write( "(2)-(1):\r
\n" ); document.write( "\n" ); document.write( "-5+4=4a-a+2b-b+c-c\r
\n" ); document.write( "\n" ); document.write( "-1=3a+b (or 3a+b=-1)\r
\n" ); document.write( "\n" ); document.write( "(3)-(1):\r
\n" ); document.write( "\n" ); document.write( "-6=8a+2b (or 4a+b=-3)\r
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\n" ); document.write( "\n" ); document.write( "taking the difference of these 2 we get\r
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\n" ); document.write( "\n" ); document.write( "4a-3a+b-b=-3+1 (or a=-2)\r
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\n" ); document.write( "\n" ); document.write( "and thus b=5\r
\n" ); document.write( "\n" ); document.write( "Now from (1):
\n" ); document.write( "-4=-2+5+c (so c=-7)\r
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\n" ); document.write( "\n" ); document.write( "y=-2x^2+5x+-7\r
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\n" ); document.write( "\n" ); document.write( ":)\r
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