document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5900>Question 5900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please explain how to solve quadratic inequalitities using sign charts.  I has me a little confused and I have about 30 problems to do.  Here is an example of one.\r<BR>\n" );
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document.write( "solve  (x-5)(x+2)>0  using a sign chart.\r<BR>\n" );
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document.write( "Thanks  Caroline </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3131 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=3131\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, understand that the (x-5)(x+2) is a quadratic, which may (or may not) cross the x-axis. So, at some points, the curve may have a -ve y-value or a +ve y-value, and this will flip at the point(s) where the curve crosses the x-axis..the root(s) of the equation.\r<BR>\n" );
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document.write( "here is this equation... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C+200%2C+-3%2C+6%2C+-12%2C+30%2C+x%5E2-3x-10%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C+200%2C+-3%2C+6%2C+-12%2C+30%2C+x%5E2-3x-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the graph, you instantly see the answers for your \"sign chart\"...\r<BR>\n" );
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document.write( "below x=-2, the curve is +ve<BR>\n" );
document.write( "Above x=+5, the curve is +ve<BR>\n" );
document.write( "between these 2 values, the curve is -ve.\r<BR>\n" );
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document.write( "So...in a sign chart - the following numbers are gotten from the equation written in its factored form, since this tells you the roots (where the curve crosses the x-axis)\r<BR>\n" );
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document.write( "x<-2__x=-2__between___x=5___x>5 <BR>\n" );
document.write( "+_______0______-______0_____+\r<BR>\n" );
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document.write( "(ignore the __ symbols...they are there to give equal spacing. Also, between is just me explaining the region between x=-2 and x=5, as i cannot write it here :-( ).\r<BR>\n" );
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document.write( "Simply, put a value, say x=+10 into the equation (x-5)(x+2) --> get (10-5)(10+2) which is (+)(+)...+ and a + makes + (we are not interested in the numerical part..just the sign.\r<BR>\n" );
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document.write( "Another example: take x=-10... (x-5)(x+2) --> (-10-5)(-10+2) --> (-)(-) --> +\r<BR>\n" );
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document.write( "Is this OK? Basically, the \"sign chart\" is to get out of sketching (not plotting) the graph, but the best thing you can ever do in any question is draw a picture, so i would concentrate on doing the sketch.\r<BR>\n" );
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document.write( "Anyway, back to the question..if it said solve (x-5)(x+2)>0, then you would know it was te 2 regions x<-2 and x>+5. etc\r<BR>\n" );
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document.write( "jon. </SPAN>\n" );
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