document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018384>Question 1018384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> justify y=x^2 using finite differences? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #634500 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=634500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> write out the following sequence<BR>\n" );
document.write( "1  4  9  16  25<BR>\n" );
document.write( "calculate the difference between the terms<BR>\n" );
document.write( " 3  5  7   9<BR>\n" );
document.write( "calculate the difference between the new terms<BR>\n" );
document.write( "  2  2  2<BR>\n" );
document.write( "On the second line, the differences are all the same, the method of finite differences tells us that the polynomial generating this sequence is of order 2<BR>\n" );
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document.write( "the general form is f(x) = ax^2 +bx +c<BR>\n" );
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document.write( "let's look at f(1), f(2), f(3)<BR>\n" );
document.write( "f(1) = a + b + c = 1<BR>\n" );
document.write( "f(2) = 4a + 2b + c = 4<BR>\n" );
document.write( "f(3) = 9a + 3b + c = 9<BR>\n" );
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document.write( "solving for a, b , c we see that a=1, b=0, c=0, therefore<BR>\n" );
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document.write( "f(x) = x^2 is our solution<BR>\n" );
document.write( ": </SPAN>\n" );
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