document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=138917>Question 138917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> heres the question: FInd a quadration function that fits the set of data points (0,-9),(-2,-13),(3,27) please help I have no idea how to do this. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101355 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=101355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> FInd a quadratic  function that fits the set of data points:<BR>\n" );
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document.write( " (0,-9),(-2,-13),(3,27)<BR>\n" );
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document.write( "One way is write 3 equations in the form: ax^2 + bx + c = y<BR>\n" );
document.write( "Find a, b, and c. We know c which is the y intercept, which occurs when x = 0<BR>\n" );
document.write( "Therefore c = -9, we only need to deal with two equations using the 2nd & 3rd coordinates<BR>\n" );
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document.write( "Substitute -2 for x and -13 for y:<BR>\n" );
document.write( "a(-2^2) + b(-2) - 9 = -13<BR>\n" );
document.write( "4a - 2b - 9 = -13<BR>\n" );
document.write( "4a - 2b = -13 + 9<BR>\n" );
document.write( "4a - 2b = -4<BR>\n" );
document.write( "Simplify, divide equation by 2<BR>\n" );
document.write( "2a - b = -2<BR>\n" );
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document.write( "The 3rd set of coordinates, Substitute 3 for x and 27 for y:<BR>\n" );
document.write( "a(3^2) + b(3) - 9 = 27<BR>\n" );
document.write( "9a + 3b = 27 + 9<BR>\n" );
document.write( "9a + 3b = 36<BR>\n" );
document.write( "Simplify, divide equation by 3<BR>\n" );
document.write( "3a + b = 12<BR>\n" );
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document.write( "Use elimination on these two equations to find a<BR>\n" );
document.write( "2a - b = -2<BR>\n" );
document.write( "3a + b = 12<BR>\n" );
document.write( "---------------adding eliminates b<BR>\n" );
document.write( "5a + 0 = 10<BR>\n" );
document.write( "a =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F5 ALIGN=MIDDLE  ALT=\"10%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = +2<BR>\n" );
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document.write( "Use the equation 3a + b = 12 to find b, substitute 2 for a<BR>\n" );
document.write( "3(2) + b = 12<BR>\n" );
document.write( "b = 12 - 6<BR>\n" );
document.write( "b = 6<BR>\n" );
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document.write( "Our equation then is: y = 2x^2 + 6x - 9<BR>\n" );
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document.write( "you should confirm this by substituting each x value of the given coordinates<BR>\n" );
document.write( "and confirm that the equation equals the given y value<BR>\n" );
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document.write( "If you follow all this, it will go a long way toward you understanding quadratic equations. You can email me if you have a question about this.<BR>\n" );
document.write( "  </SPAN>\n" );
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