document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=732968>Question 732968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rocket is propelled upward from the top of a building 220 feet tall at an initial velocity of 72 feet per second. The function that describes the height of the rocket in terms of t is f(t)=-16t^2 + 72t +220. Determine both the time at which the rocket reaches its max height and the max height that the rocket reaches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #448158 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=448158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The curve that the rocket follows is a parabola. The maximum<BR>\n" );
document.write( "height is also called the vertex of the parabola. The formula for<BR>\n" );
document.write( "the time component of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, when<BR>\n" );
document.write( "the equation looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28t%29+=+at%5E2+%2B+b%2At+%2B+c+ ALIGN=MIDDLE  ALT=\"+f%28t%29+=+at%5E2+%2B+b%2At+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this problem,<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+=+72+ ALIGN=MIDDLE  ALT=\"+b+=+72+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D+=+-72+%2F+%282%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+-72+%2F+%282%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%5Bv%5D+=+72%2F32+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+72%2F32+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bv%5D+=+2.25+ ALIGN=MIDDLE  ALT=\"+t%5Bv%5D+=+2.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "Now plug this value back into the equation to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282.25%29+ ALIGN=MIDDLE  ALT=\"+f%282.25%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282.25%29+=+-16%2A%282.25%29%5E2+%2B+72%2A2.25+%2B+220+ ALIGN=MIDDLE  ALT=\"+f%282.25%29+=+-16%2A%282.25%29%5E2+%2B+72%2A2.25+%2B+220+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282.25%29+=+-16%2A5.0625+%2B+162+%2B+220+ ALIGN=MIDDLE  ALT=\"+f%282.25%29+=+-16%2A5.0625+%2B+162+%2B+220+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282.25%29+=+-81+%2B+162+%2B+220+ ALIGN=MIDDLE  ALT=\"+f%282.25%29+=+-81+%2B+162+%2B+220+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%282.25%29+=+301+ ALIGN=MIDDLE  ALT=\"+f%282.25%29+=+301+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It reaches a maximum height of 301 ft in 2.25 sec<BR>\n" );
document.write( "Here's a plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+400%2C+400%2C+-1%2C+8%2C+-20%2C+330%2C+-16x%5E2+%2B+72x+%2B+220+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+8%2C+-20%2C+330%2C+-16x%5E2+%2B+72x+%2B+220+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );