document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314772>Question 314772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I have a few questions I'm having an extremely hard time figuring this out.  \r<BR>\n" );
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document.write( "1.  Find the vertex and intercepts of the parabola y=-3x^2+6\r<BR>\n" );
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document.write( "2.  Solve the inequality, state the solution using the interval notation and graph it.  x-3/x+5<0.\r<BR>\n" );
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document.write( "These are both for Math 209.  Thank you so much for your time and help.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225166 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=225166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The parabola is already in vertex form,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=a%28x-h%29%5E2%2Bk ALIGN=MIDDLE  ALT=\"y=a%28x-h%29%5E2%2Bk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where (h,k) is the vertex. <BR>\n" );
document.write( "It's just a bit hidden.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3x%5E2%2B6 ALIGN=MIDDLE  ALT=\"y=-3x%5E2%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-3%28x-0%29%5E2%2B6 ALIGN=MIDDLE  ALT=\"y=-3%28x-0%29%5E2%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is (0,6).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+10%2C+-3x%5E2%2B6%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-5%2C+5%2C+-5%2C+10%2C+-3x%5E2%2B6%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( " x-3/x+5<0.<BR>\n" );
document.write( "Break up the number line into 3 regions.<BR>\n" );
document.write( "Region 1: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-infinity ALIGN=MIDDLE  ALT=\"-infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 2: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "Region 3: (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "For each region, choose a point (not an endpoint) and test the inequality.<BR>\n" );
document.write( "If the inequality is solved, that region is part of the solution.<BR>\n" );
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document.write( "Region 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-10 ALIGN=MIDDLE  ALT=\"x=-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-10-3%29%2F%28-10%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%28-10-3%29%2F%28-10%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-13%29%2F%28-5%29%3C0 ALIGN=MIDDLE  ALT=\"%28-13%29%2F%28-5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F5%3C0 ALIGN=MIDDLE  ALT=\"13%2F5%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, this region is not part of the solution.<BR>\n" );
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document.write( "Region 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-3%29%2F%280%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%280-3%29%2F%280%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F5%3C0 ALIGN=MIDDLE  ALT=\"-3%2F5%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "True, this region is part of the solution.<BR>\n" );
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document.write( "Region 3: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%2F%28x%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%28x-3%29%2F%28x%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285-3%29%2F%285%2B5%29%3C0 ALIGN=MIDDLE  ALT=\"%285-3%29%2F%285%2B5%29%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F10%3C0 ALIGN=MIDDLE  ALT=\"2%2F10%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "False, this region is not part of the solution.<BR>\n" );
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document.write( "Only Region 2 is the solution region.<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+300%2C+300%2C+-10%2C+10%2C+-5%2C+5%2Cgrid%281%29%2Cblue%28line%28-5%2C10%2C-5%2C-10%29%29%2Cblue%28line%283%2C10%2C3%2C-10%29%29%2C+graph%28+300%2C+300%2C+-10%2C+10%2C+-5%2C5%2C+%28x-3%29%2F%28x%2B5%29%0D%0A+%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "The curve is below the x-axis(< 0) on in the region (-5,3). </SPAN>\n" );
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