document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=702202>Question 702202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me and explain how to solve this problem. Thank you.\r<BR>\n" );
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document.write( "The path of an arrow shot into the air is h=144t-16t^2 where h is the height in feet above the ground t seconds after it is released. Graph the equation to find what period of time the arrow is above 224 feet. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #432877 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=432877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><font face=\"Tahoma\">This equation represents a parabola,<br>\r<BR>\n" );
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document.write( "where the vertex is at a maximum,<br>\r<BR>\n" );
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document.write( "and it opens down because of the negative coefficient of t.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=144t-16t%5E2 ALIGN=MIDDLE  ALT=\"h=144t-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B144t ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B144t\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a=-16, b=144, and c=0<br>\r<BR>\n" );
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document.write( "We can easily find the vertex (h,k) if we know the proper formulae:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-b%2F2a ALIGN=MIDDLE  ALT=\"h=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-144%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"h=-144%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=9%2F2 ALIGN=MIDDLE  ALT=\"h=9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=f%28h%29 ALIGN=MIDDLE  ALT=\"k=f%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=f%289%2F2%29 ALIGN=MIDDLE  ALT=\"k=f%289%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-16%289%2F2%29%5E2%2B144%2A%289%2F2%29 ALIGN=MIDDLE  ALT=\"k=-16%289%2F2%29%5E2%2B144%2A%289%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=324 ALIGN=MIDDLE  ALT=\"k=324\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "So our vertex is the point (9/2,324)<br>\r<BR>\n" );
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document.write( "We can also find the t-intercepts,<br>\r<BR>\n" );
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document.write( "by setting h=0 and solving for t.<br>\r<BR>\n" );
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document.write( "In this case, our t-intercepts are 0 and 9.<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+600%2C+600%2C+-1%2C+10%2C+-10%2C+350%2C+-16x%5E2%2B144x+%29 ALIGN=MIDDLE  ALT=\"graph%28+600%2C+600%2C+-1%2C+10%2C+-10%2C+350%2C+-16x%5E2%2B144x+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "By inspection of the graph,<br>\r<BR>\n" );
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document.write( "it looks like the period of time that the arrow is over 224 feet<br> \r<BR>\n" );
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document.write( "is between approximately 2 seconds and 7 seconds.<br>\r<BR>\n" );
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document.write( "This is about 5 total seconds.<br>\r<BR>\n" );
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document.write( "Of course this is only an approximation!  Our graphs are never exact.<br>\r<BR>\n" );
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document.write( "To find the exact answer,<br>\r<BR>\n" );
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document.write( "we would need to find the points where h equals 224 in our equation,<br>\r<BR>\n" );
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document.write( "and then we could find the exact times.<br>\r<BR>\n" );
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document.write( "We would do this by setting the equation equal to 224, and solving for t.<br>\r<BR>\n" );
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document.write( "This would give us the extremes of the range of t-values where h was greater than 224.<br>\r<BR>\n" );
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document.write( "PS It does indeed look like 2 and 7 are the exact t-values we need.<br>\r<BR>\n" );
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document.write( "I hope this helps!  Keep practicing!  :)<br>\r<BR>\n" );
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document.write( "Thank you and good luck with all your future studies!<br><br> </SPAN>\n" );
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