document.write( "Question 1058212: Applications and Extensions
\n" ); document.write( "Curve Fitting. Find the function y=ax^2+bx+c whose graph contains the points (1,2), (-2,-7), and (2,-3) \n" ); document.write( "
Algebra.Com's Answer #673234 by Boreal(15235)\"\" \"About 
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Substitute the points into the equation
\n" ); document.write( "a+b+c=2
\n" ); document.write( "4a-2b+c=-7
\n" ); document.write( "4a+2b+c=-3
\n" ); document.write( "Look at the second and third
\n" ); document.write( "4a=2b-c-7
\n" ); document.write( "4a=-2b-c-3
\n" ); document.write( "Set those two equal to each other
\n" ); document.write( "2b-c-7=-2b-c-3
\n" ); document.write( "4b=4
\n" ); document.write( "b=1
\n" ); document.write( "Now go back to the first and substitute into one of the others.
\n" ); document.write( "a+1+c=2 or a+c=1, c=1-a
\n" ); document.write( "4a-2+1-a=-7 or 3a=-6, a=-2
\n" ); document.write( "Substitute that into the first equation.
\n" ); document.write( "-2+1+c=2; c=3
\n" ); document.write( "{-2,1,3}
\n" ); document.write( "-2x^2+bx+3=y answer
\n" ); document.write( "Try each point
\n" ); document.write( "-2+1+3=2 CHECKS
\n" ); document.write( "-8-2+3=-7 CHECKS
\n" ); document.write( "-8+2+3=-3 CHECKS
\n" ); document.write( "\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C-2x%5E2%2Bx%2B3%29\"\r
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