document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=456616>Question 456616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please please help\r<BR>\n" );
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document.write( "Find the quadraic equation that fits the following set of data points<BR>\n" );
document.write( "(5,9),(4,-45),(-1,-15) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313393 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=313393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic equation that fits the following set of data points<BR>\n" );
document.write( "(5,9),(4,-45),(-1,-15)<BR>\n" );
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document.write( "Using the form: a^2 + b^2 + c^2 = y, write an equation for each ordered pair<BR>\n" );
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document.write( "5,9<BR>\n" );
document.write( "5^2a + 5b + c = 9<BR>\n" );
document.write( "25a + 5a + c = 9<BR>\n" );
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document.write( "4,-45<BR>\n" );
document.write( "16a + 4b + c = -45<BR>\n" );
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document.write( "-1,-15<BR>\n" );
document.write( "1a - 1b + c = -15<BR>\n" );
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document.write( "You can solve this as a 3X4 matrix<BR>\n" );
document.write( "25 5 1 9<BR>\n" );
document.write( "16 4 1 -45<BR>\n" );
document.write( "1 -1 1 -15<BR>\n" );
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document.write( "but you can also use elimination/substitution, which will take longer<BR>\n" );
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document.write( "Subtract the 2nd equation from the 1st equation<BR>\n" );
document.write( "25a + 5b + c = 9<BR>\n" );
document.write( "16a + 4b + c = -45<BR>\n" );
document.write( "------------------------eliminates c<BR>\n" );
document.write( "9a + b = 54<BR>\n" );
document.write( "for substitution<BR>\n" );
document.write( "b = (54-9a)<BR>\n" );
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document.write( "Subtract the 3rd equation from the 1st equation<BR>\n" );
document.write( "25a + 5b + c = 9<BR>\n" );
document.write( "1a - 1b + c  = -15<BR>\n" );
document.write( "------------------------eliminates c again<BR>\n" );
document.write( "24a + 6b = 24<BR>\n" );
document.write( "Replace b with (54-9a)<BR>\n" );
document.write( "24a + 6(54-9a) = 24<BR>\n" );
document.write( "24a + 324 - 54a = 24<BR>\n" );
document.write( "24a - 54a = 24 - 324<BR>\n" );
document.write( "-30a = -300<BR>\n" );
document.write( "a = +10<BR>\n" );
document.write( "find b<BR>\n" );
document.write( "b = 54 - 9(10)<BR>\n" );
document.write( "b = 54 - 90<BR>\n" );
document.write( "b = -36<BR>\n" );
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document.write( "Use the 1st equation to find c<BR>\n" );
document.write( "25(10) + 5(-36) + c = 9<BR>\n" );
document.write( "250 - 180 + c = 9<BR>\n" );
document.write( "70 + c = 9<BR>\n" );
document.write( "c = 9 - 70<BR>\n" );
document.write( "c = -61<BR>\n" );
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document.write( "The equation for these ordered pairs, y = 10x^2 - 36x - 61<BR>\n" );
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document.write( "I confirmed this using the matrix feature on my calc.\r<BR>\n" );
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