document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188303>Question 188303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The profit on a watch is given by P = x2 – 13x – 80 and where x is the number of watches sold per day. How many watches were sold on a day when there was a $50 loss? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141144 by </B><A HREF=/tutors/aboutme.mpl?userid=jojo14344><B>jojo14344(1513)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jojo14344><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=141144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Tahoma\" size=1.5><BR>\n" );
document.write( "</pre><font size=4><b><BR>\n" );
document.write( "Let known <font color=blue>P=Y=Profit or  Losses</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solving for <font color=blue>\"x\"</font> for number of watches. More importantly to see the X-Intercepts.\r<BR>\n" );
document.write( "\n" );
document.write( "Given:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%5E2-13x-80 ALIGN=MIDDLE  ALT=\"P=x%5E2-13x-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By Quadratic, where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a=1%2Cb=%28-13%29%2Cc=%28-80%29%29 ALIGN=MIDDLE  ALT=\"system%28a=1%2Cb=%28-13%29%2Cc=%28-80%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Discriminant: b^2-4ac= -13^2 - 4(1)(-80)=169+320=489<BR>\n" );
document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-%28-13%29%2B-sqrt%28489%29%29%2F%282%2A1%29=%2813%2B-22.11%29%2F2 ALIGN=MIDDLE  ALT=\"x=%28-%28-13%29%2B-sqrt%28489%29%29%2F%282%2A1%29=%2813%2B-22.11%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=x=%2813%2B22.11%29%2F2=35.11%2F2=red%2817.55%29 ALIGN=MIDDLE  ALT=\"x=%2813%2B22.11%29%2F2=35.11%2F2=red%2817.55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2813-22.11%29%2F2=-9.11%2F2=red%28-4.55%29 ALIGN=MIDDLE  ALT=\"x=%2813-22.11%29%2F2=-9.11%2F2=red%28-4.55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "X-Intercepts = > <font color=blue>(17.55,0) & (-4.55,0)</font><BR>\n" );
document.write( "For Y-Intercept:<BR>\n" );
document.write( "Let fx=0 ----> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=y=0%5E2-13%280%29-80=red%28-80%29 ALIGN=MIDDLE  ALT=\"P=y=0%5E2-13%280%29-80=red%28-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Y-Intercept = > <font color=blue>(0,-80)</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We now get the vertex thru Vertex-Form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28h=x%2Ck=y%29 ALIGN=MIDDLE  ALT=\"system%28h=x%2Ck=y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Going back to our eqn:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=x%5E2-13x-80 ALIGN=MIDDLE  ALT=\"P=x%5E2-13x-80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, complete the square, by taking \"Half\" of the middle constant then \"squared\":\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In our eqn, the middle constant is 13, taking half of it = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F2=6.5 ALIGN=MIDDLE  ALT=\"13%2F2=6.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then squared it= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.5%5E2=highlight%2842.25%29 ALIGN=MIDDLE  ALT=\"6.5%5E2=highlight%2842.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We \"add\" and also \"subtract\" to the eqn:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%28x%5E2-13x%2Bhighlight%2842.25%29%29highlight%28-42.25%29-80%29 ALIGN=MIDDLE  ALT=\"P=%28x%5E2-13x%2Bhighlight%2842.25%29%29highlight%28-42.25%29-80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=%28x-6.5%29%5E2-122.25 ALIGN=MIDDLE  ALT=\"P=%28x-6.5%29%5E2-122.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > --->follows <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In our eqn, we have vertex, h=<font color=blue>x=6.5</font> & k=<font color=blue>y=-122.25</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We see graph,\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C20%2C-130%2C30%2Cgrid%281%29%2Cgraph%28500%2C500%2C-10%2C20%2C-130%2C30%2Cx%5E2-13x-80%29%2Cblue%28circle%2817.55%2C0%2C.25%29%29%2Cblue%28circle%28-4.55%2C0%2C.25%29%29%2Cblue%28circle%280%2C-80%2C.25%29%29%2C+blue%28circle%286.5%2C-122.25%2C.25%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The Y axis, is where the Profit or Losses. <BR>\n" );
document.write( "So if you have a loss of $50, that equals to <font color=red>-50</font> on the Y axis.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Make a straigth line from <font color=red>-50</font> on the Y axis  to the right until it touches the curve. As it touched the curve, extend the line downwards until it touches the X axis. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<font color=blue>This will show the number of watches for the loss sale of $50.00.</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C20%2C-130%2C30%2Cgraph%28500%2C500%2C-10%2C20%2C-130%2C30%2Cx%5E2-13x-80%29%2Cblue%28circle%2817.55%2C0%2C.25%29%29%2Cblue%28circle%28-4.55%2C0%2C.25%29%29%2Cblue%28circle%280%2C-80%2C.25%29%29%2Cgreen%28line%280%2C-50%2C15%2C-50%29%29%2Cgreen%28line%2815%2C-50%2C15%2C0%29%29%2Cred%28locate%280.3%2C-50%2C-50%29%29%2Cblue%28locate%2814%2C6%2C15=watches%29%29%2Cblue%28circle%286.5%2C-122.25%2C.25%29%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ----> <font color=red>15 watches sold</font> for a loss of $50.00\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's check,<BR>\n" );
document.write( "Go back our Eqn, & substitute x=15: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=15%5E2-13%2815%29-80=225-195-80 ALIGN=MIDDLE  ALT=\"P=15%5E2-13%2815%29-80=225-195-80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28P=-50%29 ALIGN=MIDDLE  ALT=\"highlight%28P=-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, Loss\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Thank you,<BR>\n" );
document.write( "Jojo</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );