document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149607>Question 1149607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x=3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #770939 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=770939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The derivative of the function for the given curve is the slope of the curve at any point.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3%2B2x-2x%5E2 ALIGN=MIDDLE  ALT=\"y+=+3%2B2x-2x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dy%2Fdx+=+2-2x ALIGN=MIDDLE  ALT=\"dy%2Fdx+=+2-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The slope of the given line is 1/2; we want the slope of the normal to the curve to also be 1/2.  That means we want the slope of the curve at that point to be -2.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-2x+=+-2 ALIGN=MIDDLE  ALT=\"2-2x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+2x ALIGN=MIDDLE  ALT=\"4+=+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2 ALIGN=MIDDLE  ALT=\"x+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+f%28x%29+=+3%2B2%282%29-2%5E2+=+3 ALIGN=MIDDLE  ALT=\"y+=+f%28x%29+=+3%2B2%282%29-2%5E2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The slope is 1/2; the point on the curve is (2,3).  The equation of the normal is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F2%29x%2B2 ALIGN=MIDDLE  ALT=\"y+=+%281%2F2%29x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "A graph, showing the given curve (red), the given line (green), and the normal to the curve parallel to the given line (blue).<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-2%2C4%2C-1%2C5%2C3%2B2x-x%5E2%2C.5x%2B1.5%2C.5x%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-2%2C4%2C-1%2C5%2C3%2B2x-x%5E2%2C.5x%2B1.5%2C.5x%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );