document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182154>Question 1182154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP with this graphing problem please\r<BR>\n" );
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document.write( "https://imgur.com/a/ndjmykk </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812132 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=812132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You can use a graphing tool such as GeoGebra or Desmos to graph <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+40-5x-5x%5E2 ALIGN=MIDDLE  ALT=\"y+=+40-5x-5x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note I'm using x in place of t)\r<BR>\n" );
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document.write( "Then click on the location where the curve crosses the x axis to determine the coordinates of that point. The location is approximately (2.372, 0)<BR>\n" );
document.write( "You'll only worry about cases when x > 0.\r<BR>\n" );
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document.write( "Desmos Link<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/hlyqda56a1\">https://www.desmos.com/calculator/hlyqda56a1</a><BR>\n" );
document.write( "That's the graph I set up. It's basically a parabola that's upside down.\r<BR>\n" );
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document.write( "The x coordinate of the x intercept is what we want. The 2.372 rounds to <font color=red>2.37</font> which is the only answer.\r<BR>\n" );
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document.write( "If you're not allowed to use a graphing tool, then the quadratic formula is the next best thing\r<BR>\n" );
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document.write( "y = 40 - 5x - 5x^2<BR>\n" );
document.write( "y = -5x^2 - 5x + 40<BR>\n" );
document.write( "We have something in the form y = ax^2+bx+c where<BR>\n" );
document.write( "a = -5<BR>\n" );
document.write( "b = -5<BR>\n" );
document.write( "c = 40\r<BR>\n" );
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document.write( "Those three values are plugged into the quadratic formula below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   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=x+=+%28-%28-5%29%2Bsqrt%28%28-5%29%5E2-4%28-5%29%2840%29%29%29%2F%282%28-5%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29%2Bsqrt%28%28-5%29%5E2-4%28-5%29%2840%29%29%29%2F%282%28-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-5%29-sqrt%28%28-5%29%5E2-4%28-5%29%2840%29%29%29%2F%282%28-5%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-5%29-sqrt%28%28-5%29%5E2-4%28-5%29%2840%29%29%29%2F%282%28-5%29%29\"   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=x+=+%285%2Bsqrt%28825%29%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%285%2Bsqrt%28825%29%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285-sqrt%28825%29%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%285-sqrt%28825%29%29%2F%28-10%29\"   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=x+=+%285%2B28.7228132326901%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%285%2B28.7228132326901%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285-28.7228132326901%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%285-28.7228132326901%29%2F%28-10%29\"   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=x+=+%2833.7228132326901%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%2833.7228132326901%29%2F%28-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-23.7228132326901%29%2F%28-10%29 ALIGN=MIDDLE  ALT=\"x+=+%28-23.7228132326901%29%2F%28-10%29\"   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=x+=+-3.37228132326901 ALIGN=MIDDLE  ALT=\"x+=+-3.37228132326901\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.37228132326901 ALIGN=MIDDLE  ALT=\"x+=+2.37228132326901\"   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=x+=+-3.372 ALIGN=MIDDLE  ALT=\"x+=+-3.372\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.372 ALIGN=MIDDLE  ALT=\"x+=+2.372\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We ignore the negative x value because we cannot have a negative time value. The only practical solution is roughly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+2.372 ALIGN=MIDDLE  ALT=\"x+=+2.372\"   DISABLED_style= \"max-width:90%; height:auto;\" > which rounds to <font color=red>2.37</font> as we found earlier.\r<BR>\n" );
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document.write( "Answer: <font color=red>2.37</font><BR>\n" );
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