document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206277>Question 1206277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An object is launched from a platform above the ground, the objects path is modeled with the function h(t) = -4.9t² + 19.6t + 58.8 where h(t) is the height of the object in meters above the ground and t is time in seconds.\r<BR>\n" );
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document.write( "1. Use the function to predict the height of the object after one second? [t = 1]<BR>\n" );
document.write( "2. Plug the function into Desmos. How many seconds will it take for the object to land? [h(t) = 0]<BR>\n" );
document.write( "3. How long does it take for the object to reach its maximum height? How high does it go?\r<BR>\n" );
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document.write( "1. h(1) =  ____ meters.\r<BR>\n" );
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document.write( "2. The object lands after ____ seconds.\r<BR>\n" );
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document.write( "3. The max height is ____ meters and it occurs at _____ seconds. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843592 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=843592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+19.6t+%2B+58.8+ ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+19.6t+%2B+58.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1. Use the function to predict the height of the object after one second? \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1 ALIGN=MIDDLE  ALT=\"t+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%29+=+-4.9%2A1%5E2+%2B+19.6%2A1+%2B+58.8 ALIGN=MIDDLE  ALT=\"h%281%29+=+-4.9%2A1%5E2+%2B+19.6%2A1+%2B+58.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281%29+=+73.5 ALIGN=MIDDLE  ALT=\"h%281%29+=+73.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2. Plug the function into Desmos. How many seconds will it take for the object to land? \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+0 ALIGN=MIDDLE  ALT=\"h%28t%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=-4.9t%5E2+%2B+19.6t+%2B+58.8+=0 ALIGN=MIDDLE  ALT=\"-4.9t%5E2+%2B+19.6t+%2B+58.8+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "https://www.desmos.com/calculator\r<BR>\n" );
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document.write( "or\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+-10%2C+10%2C+-10%2C+80%2C+-4.9x%5E2+%2B+19.6x+%2B+58.8%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+80%2C+-4.9x%5E2+%2B+19.6x+%2B+58.8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "from the graph we see <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%286%29+=+0 ALIGN=MIDDLE  ALT=\"h%286%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28-2%29+=+0 ALIGN=MIDDLE  ALT=\"h%28-2%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (disregard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-2 ALIGN=MIDDLE  ALT=\"t=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, time cannot be negative)\r<BR>\n" );
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document.write( "it will take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+ ALIGN=MIDDLE  ALT=\"6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >seconds for the object to land\r<BR>\n" );
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document.write( "3. How long does it take for the object to reach its maximum height? How high does it go?\r<BR>\n" );
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document.write( "find first derivative and equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >'<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28t%29=+-4.9%2A2t+%2B+19.6=-9.8+t%2B+19.6 ALIGN=MIDDLE  ALT=\"%28t%29=+-4.9%2A2t+%2B+19.6=-9.8+t%2B+19.6\"   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=-9.8+t%2B+19.6=0 ALIGN=MIDDLE  ALT=\"-9.8+t%2B+19.6=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=19.6=9.8t ALIGN=MIDDLE  ALT=\"19.6=9.8t\"   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=t=19.6%2F9.8+ ALIGN=MIDDLE  ALT=\"t=19.6%2F9.8+\"   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=t+=2 ALIGN=MIDDLE  ALT=\"t+=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it will take <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec for the object to reach its maximum heigh\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-4.9%2A2%5E2+%2B+19.6%2A2+%2B+58.8 ALIGN=MIDDLE  ALT=\"h%282%29+=+-4.9%2A2%5E2+%2B+19.6%2A2+%2B+58.8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+78.4+ ALIGN=MIDDLE  ALT=\"h%282%29+=+78.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >meters\r<BR>\n" );
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document.write( "2. The object lands after <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.\r<BR>\n" );
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document.write( "3. The max height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78.4 ALIGN=MIDDLE  ALT=\"78.4\"   DISABLED_style= \"max-width:90%; height:auto;\" > meters and it occurs at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2 ALIGN=MIDDLE  ALT=\"t=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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