document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122161>Question 122161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is launched into the air.  The height in feet, of the rocket, above the ground is given by h(t)=-4.9t(squared) + 192t, where t represents the time in seconds after the launch.  (Hint:draw a picture) <BR>\n" );
document.write( "#1.  How long is the rocket in the air before it reaches the ground?<BR>\n" );
document.write( "#2.  How long does it take the rocket to reach its highest point?<BR>\n" );
document.write( "#3.  How high is the rocket at its highest point?  I know that to find this answer I use the formula for the line of symmetry, and the vertex is the highest point..I think that it is 19.6 feet if I did it right.\r<BR>\n" );
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document.write( "The other questions I do not know how to do.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #89679 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=89679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I can plot this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-5%2C+50%2C+-50%2C+2000%2C+%28-4.9%29%2Ax%5E2+%2B+192x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-5%2C+50%2C+-50%2C+2000%2C+%28-4.9%29%2Ax%5E2+%2B+192x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+192t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+192t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "(1) I need to find the change in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > when th3e <BR>\n" );
document.write( "rocket goes from (t,h) = (0,0) to (t,0) where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the <BR>\n" );
document.write( "time to fall back to earth<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-4.9t%5E2+%2B+192t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-4.9t%5E2+%2B+192t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-4.9t%5E2+%2B+192t ALIGN=MIDDLE  ALT=\"0+=+-4.9t%5E2+%2B+192t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%28-4.9%2At+%2B+192%29+=+0 ALIGN=MIDDLE  ALT=\"t%2A%28-4.9%2At+%2B+192%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+0 ALIGN=MIDDLE  ALT=\"t+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the point (0,0)<BR>\n" );
document.write( "The other solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4.9%2At+%2B+192+=+0 ALIGN=MIDDLE  ALT=\"-4.9%2At+%2B+192+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.9%2At+=+192 ALIGN=MIDDLE  ALT=\"4.9%2At+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+39.184 ALIGN=MIDDLE  ALT=\"t+=+39.184\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec (this agrees closely with graph)<BR>\n" );
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document.write( "(2) The highest point is where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"t+=+%28-b%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > when<BR>\n" );
document.write( "equation is in the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ax%5E2+%2B+bx+%2B+c+=+0 ALIGN=MIDDLE  ALT=\"+ax%5E2+%2B+bx+%2B+c+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+-4.9 ALIGN=MIDDLE  ALT=\"a+=+-4.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+192 ALIGN=MIDDLE  ALT=\"b+=+192\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-192%29+%2F+%28-9.8%29 ALIGN=MIDDLE  ALT=\"t+=+%28-192%29+%2F+%28-9.8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+19.592 ALIGN=MIDDLE  ALT=\"t+=+19.592\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec (this is exactly 1/2 the time to hit the ground)<BR>\n" );
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document.write( "(3) I need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bt%5D ALIGN=MIDDLE  ALT=\"h%5Bt%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+19.592 ALIGN=MIDDLE  ALT=\"t+=+19.592\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bmax%5D+=+-4.9t%5E2+%2B+192t ALIGN=MIDDLE  ALT=\"h%5Bmax%5D+=+-4.9t%5E2+%2B+192t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bmax%5D+=+-4.9%2A%2819.592%29%5E2+%2B+192%2A%2819.592%29 ALIGN=MIDDLE  ALT=\"h%5Bmax%5D+=+-4.9%2A%2819.592%29%5E2+%2B+192%2A%2819.592%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bmax%5D+=+-1880.848+%2B+3761.664 ALIGN=MIDDLE  ALT=\"h%5Bmax%5D+=+-1880.848+%2B+3761.664\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bmax%5D+=+1880.816 ALIGN=MIDDLE  ALT=\"h%5Bmax%5D+=+1880.816\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft (this agrees with graph, also)   </SPAN>\n" );
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