document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204125>Question 204125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I've been instructed to find the general equation given this information: zeros at (-1-sqrt(3)) and (-1+sqrt(3)). A point intersected by the parabola of this equation is (1,2). I have determined that a=-(2/3). \r<BR>\n" );
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document.write( "I now have the equation -(2/3)*(x-1-sqrt(3))*(x-1+sqrt(3)). I'm supposed to find the general equation, \"fully expanded, in descending order of powers\". I've tried simplifying this equation - i.e. factoring - but cannot find a 'simpler' equation that goes through the point (1,2). I did graph the equation I'm trying to simplify, and it does indeed go through (1,2). So, my question is, can this equation be simplified further, or do I have my answer? If this can be simplified further, would you please show me how? Thank you very much!  Julia. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154085 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154085\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) =  -(2/3)*(x-1-sqrt(3))*(x-1+sqrt(3))<BR>\n" );
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document.write( "f(x) = (-2/3)<BR>\n" );
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document.write( "Notice that that factors are now in the form (a-b)(a+b)<BR>\n" );
document.write( "which multiplies to be a^2-b^2.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "f(x) = (-2/3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = (-2/3)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "f(x) = (-2/3)(x^2-2x-2)<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
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