document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028737>Question 1028737</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me! Thanks (:\r<BR>\n" );
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document.write( "Approximate the zeros of the function. Round to the nearest tenth. \r<BR>\n" );
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document.write( "1.) y=x^2-7x+7\r<BR>\n" );
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document.write( "2.) y=-2x^2-9x+10\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643908 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=643908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We use Newton's method to approximate zeros<BR>\n" );
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document.write( "x(n+1) = x(n) - (f(x(n)) / f'(x(n)))<BR>\n" );
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document.write( "1) y = x^2-7x+7<BR>\n" );
document.write( "Consider the graph of this equation<BR>\n" );
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document.write( "The zeros are close to 1 and 6, I will show you how to find the zero close to 1.  All others follow the same procedure.<BR>\n" );
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document.write( "Calculate f'<BR>\n" );
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document.write( "f' = 2x-7<BR>\n" );
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document.write( "Let x(0) = 1, then<BR>\n" );
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document.write( "x(1) = x(0) - (f(x(0)) / f'(x(0))<BR>\n" );
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document.write( "x(1) = 1 - (1 / -5) = 1.2<BR>\n" );
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document.write( "x(2) = 1.2 - (0.04 / -4.6) approx 1.2<BR>\n" );
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document.write( "Since x(2) = x(1), there is no point in continuing<BR>\n" );
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document.write( "f(1.2) = 0.04 approximately 0.0, therefore<BR>\n" );
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document.write( "x = 1.2 is a good approximation for a zero<BR>\n" );
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