document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697309>Question 697309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function  . \r<BR>\n" );
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document.write( "h(t)=100t-16t^2\r<BR>\n" );
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document.write( "What is the maximum height that the ball will reach? Height= ? feet\r<BR>\n" );
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document.write( "Do not round your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429862 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=429862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plot this function with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+ ALIGN=MIDDLE  ALT=\"+h%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the vertical axis<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the horizontal axis.<BR>\n" );
document.write( "This is a parabola that has a maximum. The maximum is<BR>\n" );
document.write( "half-way between the 2 roots. One of the roots is at <BR>\n" );
document.write( "(0,0) at the instant the ball was thrown upward.<BR>\n" );
document.write( "Find the other root by setting <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;\" > , and<BR>\n" );
document.write( "find the time when the ball comes back to the ground.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+100t+-+16t%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+100t+-+16t%5E2+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50t+-+8t%5E2+=+0+ ALIGN=MIDDLE  ALT=\"+50t+-+8t%5E2+=+0+\"   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+50+-+8t+%29+=+0+ ALIGN=MIDDLE  ALT=\"+t%2A%28+50+-+8t+%29+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+-+8t+=+0+ ALIGN=MIDDLE  ALT=\"+50+-+8t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8t+=+50+ ALIGN=MIDDLE  ALT=\"+8t+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+25%2F4+ ALIGN=MIDDLE  ALT=\"+t+=+25%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The time half-way between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+ ALIGN=MIDDLE  ALT=\"+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2F4+ ALIGN=MIDDLE  ALT=\"+25%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+25%2F8+ ALIGN=MIDDLE  ALT=\"+25%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now find the height at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+25%2F8+ ALIGN=MIDDLE  ALT=\"+t+=+25%2F8+\"   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+=+100t+-+16t%5E2+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+100t+-+16t%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2825%2F8%29+=+100%2A%2825%2F8%29+-+16%2A%2825%2F8%29%5E2+ ALIGN=MIDDLE  ALT=\"+h%2825%2F8%29+=+100%2A%2825%2F8%29+-+16%2A%2825%2F8%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2825%2F8%29+=+12.5%2A25+-+16%2A%28625%2F64%29+ ALIGN=MIDDLE  ALT=\"+h%2825%2F8%29+=+12.5%2A25+-+16%2A%28625%2F64%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%2825%2F8%29+=+312.5+-+625%2F4+ ALIGN=MIDDLE  ALT=\"+h%2825%2F8%29+=+312.5+-+625%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2825%2F8%29+=+312.5+-+156.25+ ALIGN=MIDDLE  ALT=\"+h%2825%2F8%29+=+312.5+-+156.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%2825%2F8%29+=+156.25+ ALIGN=MIDDLE  ALT=\"+h%2825%2F8%29+=+156.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximum height is 156.25 ft<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-2%2C+8%2C+-20%2C+200%2C+-16x%5E2+%2B+100x+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+8%2C+-20%2C+200%2C+-16x%5E2+%2B+100x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );