document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150290>Question 1150290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic Equation that fits the following set of Data points. (5,162),(4,110),(1,14) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #771674 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=771674\">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. (5,162),(4,110),(1,14)<BR>\n" );
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document.write( "using the form: ax^2 + bx + c = y<BR>\n" );
document.write( "x=5, y=162<BR>\n" );
document.write( "25a + 5b + c = 162<BR>\n" );
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document.write( "x=4; y=110<BR>\n" );
document.write( "16a + 4b + c = 110<BR>\n" );
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document.write( "x=1, y=14<BR>\n" );
document.write( "a + b + c = 14<BR>\n" );
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document.write( "use elimination on 1st two equations<BR>\n" );
document.write( "25a + 5b + c = 162<BR>\n" );
document.write( "16a + 4b + c = 110<BR>\n" );
document.write( "--------------------subtraction eliminates c<BR>\n" );
document.write( "9a + b = 52<BR>\n" );
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document.write( "use elimination on last two equations<BR>\n" );
document.write( "16a + 4b + c = 110<BR>\n" );
document.write( " a +   b + c = 14<BR>\n" );
document.write( "--------------------subtraction eliminates c<BR>\n" );
document.write( "15a + 3b = 96<BR>\n" );
document.write( "simplify divide by 3<BR>\n" );
document.write( "5a + b = 32<BR>\n" );
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document.write( "use elimination on the resulting two equations<BR>\n" );
document.write( "9a + b = 52<BR>\n" );
document.write( "5a + b = 32<BR>\n" );
document.write( "--------------subtraction eliminates b<BR>\n" );
document.write( "4a = 20<BR>\n" );
document.write( "a = 5<BR>\n" );
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document.write( "substituting 5 for a in the 1st two equations<BR>\n" );
document.write( "125 + 5b + c = 162<BR>\n" );
document.write( "5b + c = 162 - 125<BR>\n" );
document.write( "5b + c = 37<BR>\n" );
document.write( "and<BR>\n" );
document.write( "80 + 4b + c = 110<BR>\n" );
document.write( "4b + c = 110 - 80<BR>\n" );
document.write( "4b + c = 30<BR>\n" );
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document.write( "using elimination in these two equations<BR>\n" );
document.write( "5b + c = 37<BR>\n" );
document.write( "4b + c = 30<BR>\n" );
document.write( "-------------subtraction eliminates c<BR>\n" );
document.write( "b = 7<BR>\n" );
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document.write( "use the last original equation to find c<BR>\n" );
document.write( "5 + 7 + c = 14<BR>\n" );
document.write( "c = 14 - 12<BR>\n" );
document.write( "c = 2<BR>\n" );
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document.write( "The equation for the given points:<BR>\n" );
document.write( "y = 5x^2 + 7x + 2<BR>\n" );
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document.write( "I'll let you confirm this is true </SPAN>\n" );
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