document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177975>Question 1177975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation of the parabola of the form y=ax^2+bx+c that passes through the following three points.<BR>\n" );
document.write( "(1,2),(-1,6),(3,6) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807132 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the equation of the parabola be y=ax2+bx+c.\r<BR>\n" );
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document.write( " the parabola passes through the point  plug  plug (1,2), then 2=a+b+c.\r<BR>\n" );
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document.write( "the parabola passes through the point (−1,6), then 6=a−b+c.\r<BR>\n" );
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document.write( "the parabola passes through the point plug (3,6), then 6=9a+3b+c.\r<BR>\n" );
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document.write( "Thus, we have obtained the following system with three variables<BR>\n" );
document.write( "⎧⎩⎨a+b+c=2<BR>\n" );
document.write( "a−b+c=69<BR>\n" );
document.write( "a+3b+c=6\r<BR>\n" );
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document.write( "Solving the system of linear equations , we get that a=1, b=−2, c=3.\r<BR>\n" );
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document.write( "Therefore the equation of the parabola is y=x2−2x+3.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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