document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=745110>Question 745110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height s, in feet, of a rock thrown upward at an initial speed of  64 ft/sec from a cliff 50 ft above an ocean beach is given by the function s(t)=-16t^2+64t+50, where t is the time in seconds. Find the maximum height above the beach that the rock will attain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #453737 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=453737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The maximum height of this parabolic curve is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+s%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+t+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "the equation has the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%28t%29+=+at%5E2+%2B+b%2At+%2B+c+ ALIGN=MIDDLE  ALT=\"+s%28t%29+=+at%5E2+%2B+b%2At+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In your equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%28t%29+=+-16t%5E2+%2B+64t+%2B+50+ ALIGN=MIDDLE  ALT=\"+s%28t%29+=+-16t%5E2+%2B+64t+%2B+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+-16+ ALIGN=MIDDLE  ALT=\"+a+=+-16+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+64+ ALIGN=MIDDLE  ALT=\"+b+=+64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-64+%2F+%28+2%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+-64+%2F+%28+2%2A%28-16%29%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+=+-64+%2F+-32+ ALIGN=MIDDLE  ALT=\"+t+=+-64+%2F+-32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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;\" > sec<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%282%29+ ALIGN=MIDDLE  ALT=\"+s%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the maximum height<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s%282%29+=+-16%2A2%5E2+%2B+64%2A2+%2B+50+ ALIGN=MIDDLE  ALT=\"+s%282%29+=+-16%2A2%5E2+%2B+64%2A2+%2B+50+\"   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+128+%2B+50+ ALIGN=MIDDLE  ALT=\"+s%282%29+=+-64+%2B+128+%2B+50+\"   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+=+114+ ALIGN=MIDDLE  ALT=\"+s%282%29+=+114+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft<BR>\n" );
document.write( "The maximum height is 114 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+5%2C+-10%2C+130%2C+-16x%5E2+%2B+64x+%2B+50+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+5%2C+-10%2C+130%2C+-16x%5E2+%2B+64x+%2B+50+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );