document.write( "Question 120149: dear tutor: please help! i have a question where x = 2,4,6,8,10 and y = 3,8,15,24,35. what would the equation be that would match this graph? thanks, joe \n" ); document.write( "

Algebra.Com's Answer #88109 by scott8148(6628) $\"\"$ $\"About$

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the differences in x are constant (2)\r
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\n" ); document.write( "\n" ); document.write( "the differences in y are 5, 7, 9, 11 __ but the differences in the differences are constant (2)\r
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\n" ); document.write( "\n" ); document.write( "this indicates a second order (squared) relation\r
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\n" ); document.write( "\n" ); document.write( "y=ax^2+bx+c\r
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\n" ); document.write( "\n" ); document.write( "for (2,3) 3=4a+2b+c
\n" ); document.write( "for (4,8) 8=16a+4b+c
\n" ); document.write( "for (6,15) 15=36a+6b+c\r
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\n" ); document.write( "\n" ); document.write( "subtracting first from second gives 5=12a+2b (A)
\n" ); document.write( "subtracting second from third gives 7=20a+2b (B)\r
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\n" ); document.write( "\n" ); document.write( "subtracting (A) from (B) gives 2=8a, so a=.25\r
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\n" ); document.write( "\n" ); document.write( "substituting gives 5=12(.25)+2b __ 2=2b __ 1=b\r
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\n" ); document.write( "\n" ); document.write( "substituting gives 3=4(.25)+2(1)+c __ 3=1+2+c __ 0=c\r
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\n" ); document.write( "\n" ); document.write( "y=.25x^2+x \n" ); document.write( "

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