document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924934>Question 924934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, \r<BR>\n" );
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document.write( "I'm having trouble with this question from my A level Integration module;\r<BR>\n" );
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document.write( "Find the equation for a quadratic curve that passes through O(0,0) and its gradient at the point (-2,3) is -1.\r<BR>\n" );
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document.write( "I can integrate a differentiated function to get it's original, but without the differential I'm stuck on this and can't see where to begin.\r<BR>\n" );
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document.write( "Thanks, \r<BR>\n" );
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document.write( "R </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #561206 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=561206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadratic curve : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Passes through the origin : <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=a%280%29%2Bb%280%29%2Bc ALIGN=MIDDLE  ALT=\"0=a%280%29%2Bb%280%29%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax%5E2%2Bbx ALIGN=MIDDLE  ALT=\"y=ax%5E2%2Bbx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The derivative of the function is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=2ax%2Bb ALIGN=MIDDLE  ALT=\"dy%2Fdx=2ax%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The function also passes through (-2,3) where, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx=-1 ALIGN=MIDDLE  ALT=\"dy%2Fdx=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%28-2%29%2Bb=-1 ALIGN=MIDDLE  ALT=\"2a%28-2%29%2Bb=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4a%2Bb=-1 ALIGN=MIDDLE  ALT=\"-4a%2Bb=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But also from the value of the function,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a%28-2%29%5E2%2Bb%28-2%29 ALIGN=MIDDLE  ALT=\"3=a%28-2%29%5E2%2Bb%28-2%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=4a-2b=3 ALIGN=MIDDLE  ALT=\"4a-2b=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add eq. 1 to eq. 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4a%2Bb%2B4a-2b=-1%2B3 ALIGN=MIDDLE  ALT=\"-4a%2Bb%2B4a-2b=-1%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-b=2 ALIGN=MIDDLE  ALT=\"-b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4a-2=-1 ALIGN=MIDDLE  ALT=\"-4a-2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4a=1 ALIGN=MIDDLE  ALT=\"-4a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1%2F4 ALIGN=MIDDLE  ALT=\"a=-1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%281%2F4%29x%5E2-2x%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%281%2F4%29x%5E2-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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