document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193889>Question 1193889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825946 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=825946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the quadratic function that fits the data points (1,6) (-1,2) and (3,34).<BR>\n" );
document.write( "Using the form ax^2 + bx + c = y, write an equation for each x,y point<BR>\n" );
document.write( "1,6:  a + b + c = 6<BR>\n" );
document.write( "-1,2: a - b + c = 2<BR>\n" );
document.write( "3,34: 9a+3b + c = 34<BR>\n" );
document.write( ":<BR>\n" );
document.write( "add the 1st 2 equations<BR>\n" );
document.write( " a + b + c = 6<BR>\n" );
document.write( " a - b + c = 2<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "2a + 0 + 2c = 8<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "a + c = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply the 2nd equation by 3, add to the 3rd equation<BR>\n" );
document.write( "3a - 3b + 3c = 6<BR>\n" );
document.write( "9a + 3b +  c = 34<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "12a + 0 + 4c = 40<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "6a + 2c = 20<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Multiply (a+c=4) by 2, subtract from the above equation<BR>\n" );
document.write( "6a + 2c = 20<BR>\n" );
document.write( "2a + 2c = 8<BR>\n" );
document.write( "--------------subtraction eliminates c, find a<BR>\n" );
document.write( "4a + 0 = 12<BR>\n" );
document.write( "a = 12/4<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a + c = 4<BR>\n" );
document.write( "3 + c = 4<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "a + b + c = 6<BR>\n" );
document.write( "3 + b + 1 = 6<BR>\n" );
document.write( "b = 6 - 4<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The equation: y = 3x^2 + 2x + 1<BR>\n" );
document.write( " </SPAN>\n" );
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