document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=47784>Question 47784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maximum height. If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t)= -16t^2 + 32t where t is time in seconds. Graph this parabola for 0 =< t =< 2. What is the maximum height reached by the ball?\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 #31588 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=31588\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29=+-16t%5E2+%2B+32t ALIGN=MIDDLE  ALT=\"s%28t%29=+-16t%5E2+%2B+32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "At t = 0, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%280%29+=+0 ALIGN=MIDDLE  ALT=\"s%280%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > because the height is zero.<BR>\n" );
document.write( "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;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28t%29+=+0 ALIGN=MIDDLE  ALT=\"s%28t%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > also because<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29=+-16%2A%282%5E2%29+%2B+32%2A2 ALIGN=MIDDLE  ALT=\"s%282%29=+-16%2A%282%5E2%29+%2B+32%2A2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29=+-64+%2B+64 ALIGN=MIDDLE  ALT=\"s%282%29=+-64+%2B+64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%282%29+=+0 ALIGN=MIDDLE  ALT=\"s%282%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 2 sec the ball lands back on the ground.<BR>\n" );
document.write( "The max height is midway between 0 and 2, which is 1,<BR>\n" );
document.write( "so in 1 sec the ball reaches its max height, and the<BR>\n" );
document.write( "max height is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29=+-16%2A%281%5E2%29+%2B+32%2A1 ALIGN=MIDDLE  ALT=\"s%281%29=+-16%2A%281%5E2%29+%2B+32%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+-16+%2B+32 ALIGN=MIDDLE  ALT=\"s%281%29+=+-16+%2B+32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%281%29+=+16 ALIGN=MIDDLE  ALT=\"s%281%29+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The max height is 16 feet<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-1%2C+4%2C+-2%2C+20%2C+-16%2A%28x%5E2%29+%2B+32x%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-1%2C+4%2C+-2%2C+20%2C+-16%2A%28x%5E2%29+%2B+32x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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