document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=735792>Question 735792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function s = -16t^2 + 64t + 512 gives the position (in feet) of a rocket fired upward from an initial height of 512 feet above the ground\r<BR>\n" );
document.write( "\n" );
document.write( "a)How long does it take for the rocket to reach its maximum height?<BR>\n" );
document.write( "b)What is the maximum height obtained by the rocket?<BR>\n" );
document.write( "c)How long does it take for the rocket to reach the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #449547 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=449547\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation has the general form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-coordinate of the vertex is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In the given equation:<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+=+2+ ALIGN=MIDDLE  ALT=\"+t+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) The rocket takes 2 sec to reach maximum height<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s ALIGN=MIDDLE  ALT=\"s\"   DISABLED_style= \"max-width:90%; height:auto;\" > when <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+-16t%5E2+%2B+64t+%2B+512+ ALIGN=MIDDLE  ALT=\"+s+=+-16t%5E2+%2B+64t+%2B+512+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+-16%2A2%5E2+%2B+64%2A2+%2B+512+ ALIGN=MIDDLE  ALT=\"+s+=+-16%2A2%5E2+%2B+64%2A2+%2B+512+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+-64+%2B+128+%2B+512+ ALIGN=MIDDLE  ALT=\"+s+=+-64+%2B+128+%2B+512+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+576+ ALIGN=MIDDLE  ALT=\"+s+=+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(b) At the vertex, the height is 576 ft above ground<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Find <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 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+s+=+0+ ALIGN=MIDDLE  ALT=\"+s+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+-16t%5E2+%2B+64t+%2B+512+ ALIGN=MIDDLE  ALT=\"+0+=+-16t%5E2+%2B+64t+%2B+512+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t%5E2+%2B+4t+%2B+32+ ALIGN=MIDDLE  ALT=\"+-t%5E2+%2B+4t+%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=+%28+-t+%2B+8+%29%2A%28+t+%2B+4+%29+ ALIGN=MIDDLE  ALT=\"+%28+-t+%2B+8+%29%2A%28+t+%2B+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( I could see these were factors )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+8+ ALIGN=MIDDLE  ALT=\"+t+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( ignore other solution-can't have negative time )<BR>\n" );
document.write( "(c) In 8 sec, the rocket reaches the ground<BR>\n" );
document.write( "---------------<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+-3%2C+10%2C+-30%2C+625%2C+-16x%5E2+%2B+64x+%2B+512+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-3%2C+10%2C+-30%2C+625%2C+-16x%5E2+%2B+64x+%2B+512+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );