document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1047772>Question 1047772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you help me make my a new quadratic function word problem and give the solution?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #663340 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=663340\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Example : <BR>\n" );
document.write( "The length of a rectangle is three more than twice the width.  Determine the dimensions that will give a total area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27m%5E2 ALIGN=MIDDLE  ALT=\"27m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Solution: \r<BR>\n" );
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document.write( "First we need to draw a picture to visualize the problem. Since the length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > more that twice the width, we will have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=2w%2B3 ALIGN=MIDDLE  ALT=\"l=2w%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So we have the following picture:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Aline%281%2C0%2C6%2C0%29%2Cline%281%2C3%2C6%2C3%29%2Cline%281%2C0%2C1%2C3%29%2Cline%286%2C3%2C6%2C0%29%2C%0D%0Alocate%286.2%2C2%2Cw%29%2Clocate%283%2C3.5%2Cl=2w%2B3%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now, since both parts of this question deal with the area of this rectangle, lets begin by generating a function for the area.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=wl ALIGN=MIDDLE  ALT=\"A=wl\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have:  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=w%282w%2B3%29 ALIGN=MIDDLE  ALT=\"A=w%282w%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2w%5E2%2B3w ALIGN=MIDDLE  ALT=\"A=2w%5E2%2B3w\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First, we want to know what dimensions make an area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27m%5E2 ALIGN=MIDDLE  ALT=\"27m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Thus, we can insert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A ALIGN=MIDDLE  ALT=\"+A\"   DISABLED_style= \"max-width:90%; height:auto;\" > into our function and solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "We have: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27=2w%5E2%2B3w ALIGN=MIDDLE  ALT=\"27=2w%5E2%2B3w\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B3w-27=0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B3w-27=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B9w-6w-27=0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B9w-6w-27=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w%5E2-6w%29%2B%289w-27%29=0 ALIGN=MIDDLE  ALT=\"%282w%5E2-6w%29%2B%289w-27%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%28w-3%29%2B9%28w-3%29=0 ALIGN=MIDDLE  ALT=\"2w%28w-3%29%2B9%28w-3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-3%29+%282w%2B9%29+=+0 ALIGN=MIDDLE  ALT=\"%28w-3%29+%282w%2B9%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-3%29++=+0 ALIGN=MIDDLE  ALT=\"%28w-3%29++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=3 ALIGN=MIDDLE  ALT=\"w=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w%2B9%29+=+0+ ALIGN=MIDDLE  ALT=\"%282w%2B9%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-9%2F2 ALIGN=MIDDLE  ALT=\"w=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > represents the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width ALIGN=MIDDLE  ALT=\"width\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a rectangle we must omit the negative value.Therefore, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=3 ALIGN=MIDDLE  ALT=\"w=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Plugging that value into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=2w%2B3 ALIGN=MIDDLE  ALT=\"l=2w%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=2%2A3%2B3 ALIGN=MIDDLE  ALT=\"l=2%2A3%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l=9 ALIGN=MIDDLE  ALT=\"l=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the dimensions that give the rectangle an area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27m%5E2 ALIGN=MIDDLE  ALT=\"27m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9m ALIGN=MIDDLE  ALT=\"9m\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3m ALIGN=MIDDLE  ALT=\"3m\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );