document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=320057>Question 320057</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the vertex and line of semmetry of  f(x)=-3(x+2)^2<BR>\n" );
document.write( "graph the function<BR>\n" );
document.write( "thanks in advance\r<BR>\n" );
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document.write( "solve for x<BR>\n" );
document.write( "4x^2=-9x-2\r<BR>\n" );
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document.write( "solve by completing the square<BR>\n" );
document.write( "x^2 + 13/2x =13\r<BR>\n" );
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document.write( "the width of a rectangle is 2ft less . the area is 15ft^2. find the lenghth and width... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #229250 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=229250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation is already in vertex form, <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;\" >, where (h,k) is the vertex.<BR>\n" );
document.write( "Comparing<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%2B2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-3%28x%2B2%29%5E2%2B0 ALIGN=MIDDLE  ALT=\"f%28x%29=-3%28x%2B2%29%5E2%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "(h,k)=(-2,0).<BR>\n" );
document.write( "The axis of symmetry includes the vertex.<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>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-5%2C5%2Cgrid%281%29%2Ccircle%28-2%2C0%2C.3%29%2Cblue%28line%28-2%2C-10%2C-2%2C10%29%29%2Cgraph%28300%2C300%2C-5%2C5%2C-5%2C5%2C-3%28x%2B2%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2=-9x-2 ALIGN=MIDDLE  ALT=\"4x%5E2=-9x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B9x%2B2=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B9x%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2%2B%289%2F4%29x%29%2B2=0 ALIGN=MIDDLE  ALT=\"4%28x%5E2%2B%289%2F4%29x%29%2B2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%5E2%2B%289%2F4%29x%2B81%2F64%29%2B2-81%2F16=0 ALIGN=MIDDLE  ALT=\"4%28x%5E2%2B%289%2F4%29x%2B81%2F64%29%2B2-81%2F16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B9%2F8%29%5E2-49%2F16=0 ALIGN=MIDDLE  ALT=\"4%28x%2B9%2F8%29%5E2-49%2F16=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B9%2F8%29%5E2=49%2F16 ALIGN=MIDDLE  ALT=\"4%28x%2B9%2F8%29%5E2=49%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B9%2F8%29%5E2=49%2F64 ALIGN=MIDDLE  ALT=\"%28x%2B9%2F8%29%5E2=49%2F64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B9%2F8=0+%2B-+7%2F8 ALIGN=MIDDLE  ALT=\"x%2B9%2F8=0+%2B-+7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-9%2F8+%2B-+7%2F8 ALIGN=MIDDLE  ALT=\"x=-9%2F8+%2B-+7%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-2%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-1%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-1%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%2813%2F2%29x+=13 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%2813%2F2%29x+=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%2813%2F2%29x+%2B%2813%2F4%29%5E2=13%2B%2813%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%2813%2F2%29x+%2B%2813%2F4%29%5E2=13%2B%2813%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%2813%2F4%29%29%5E2=208%2F16%2B169%2F16 ALIGN=MIDDLE  ALT=\"%28x%2B%2813%2F4%29%29%5E2=208%2F16%2B169%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B%2813%2F4%29%29%5E2=377%2F16 ALIGN=MIDDLE  ALT=\"%28x%2B%2813%2F4%29%29%5E2=377%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B13%2F4=0+%2B-+sqrt%28377%29%2F4 ALIGN=MIDDLE  ALT=\"x%2B13%2F4=0+%2B-+sqrt%28377%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=-13%2F4+%2B-+sqrt%28377%29%2F4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=-13%2F4+%2B-+sqrt%28377%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "For a rectangle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=15 ALIGN=MIDDLE  ALT=\"A=L%2AW=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=L-2 ALIGN=MIDDLE  ALT=\"W=L-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2A%28L-2%29=15 ALIGN=MIDDLE  ALT=\"L%2A%28L-2%29=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2-2L=15 ALIGN=MIDDLE  ALT=\"L%5E2-2L=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2-2L-15=0 ALIGN=MIDDLE  ALT=\"L%5E2-2L-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L-5%29%28L%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28L-5%29%28L%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Only the positive solution makes sense in this problem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L-5=0 ALIGN=MIDDLE  ALT=\"L-5=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=5%29 ALIGN=MIDDLE  ALT=\"highlight%28L=5%29\"   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=W=L-2 ALIGN=MIDDLE  ALT=\"W=L-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=5-2 ALIGN=MIDDLE  ALT=\"W=5-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28W=3%29 ALIGN=MIDDLE  ALT=\"highlight%28W=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );