document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=11671>Question 11671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE ANSWER ASAP!!!!<BR>\n" );
document.write( "Points A and B are on a parabola y = 4x^2+ 7x -1 and the origin is the midpoint of AB.  <BR>\n" );
document.write( "***What is the length of AB? \r<BR>\n" );
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document.write( "THANK YOU!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5992 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=5992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Let A = (xo,yo) ,B = (x1,y1),then  their midpoint is<BR>\n" );
document.write( "  ((xo+x1)/2,(yo+y1)/2) = (0,0).<BR>\n" );
document.write( " So x1=-x0,y1=-yo.<BR>\n" );
document.write( " <BR>\n" );
document.write( " Since A,B are both on the  the parabola, <BR>\n" );
document.write( " we have yo = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4xo%5E2%2B+7xo+-1 ALIGN=MIDDLE  ALT=\"+4xo%5E2%2B+7xo+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...(1) and<BR>\n" );
document.write( " -yo = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4xo%5E2-+7xo+-1 ALIGN=MIDDLE  ALT=\"4xo%5E2-+7xo+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >...(2)<BR>\n" );
document.write( " <BR>\n" );
document.write( " (1)+(2): 0 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8x0%5E2+-2 ALIGN=MIDDLE  ALT=\"+8x0%5E2+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " So, xo = 1/2 or -1/2<BR>\n" );
document.write( " and hence,yo = 4(1/4) - 7/2 - 1= -7/2 <BR>\n" );
document.write( "  or yo = 7/2<BR>\n" );
document.write( " <BR>\n" );
document.write( " Let O be the origin.<BR>\n" );
document.write( " We see that  the length of AB = 2 distance of OA<BR>\n" );
document.write( " = 2<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++sqrt%28%281%2F2%29%5E2+%2B+%287%2F2%29%5E2%29+ ALIGN=MIDDLE  ALT=\"++sqrt%28%281%2F2%29%5E2+%2B+%287%2F2%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " = 2 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%2850%29%2F2 ALIGN=MIDDLE  ALT=\"+sqrt%2850%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( " = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%2850%29 ALIGN=MIDDLE  ALT=\"+sqrt%2850%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( " Kenny<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );