document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=811813>Question 811813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h = -16t^2+vt+s, where h is in feet. If the object is propelled from a height of 12 feet with an initial velocity of 96 feet per second, its height h is given by the equation h = 16t^2+64t+8. After how many seconds is the height is 120 feet? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488935 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=488935\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since this is a parabola, there will likely<BR>\n" );
document.write( "be 2 solutions. One solution is the time <BR>\n" );
document.write( "when the object is on it's way up and reaches<BR>\n" );
document.write( "120 ft. The other solution is the time when<BR>\n" );
document.write( "the object is on it's way down and reaches<BR>\n" );
document.write( "120 ft again.<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+%2B+64t+%2B+8+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+64t+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( actually, it looks like the 8 should be a 12,<BR>\n" );
document.write( "which is the initial height, but I'll leave it 8 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+120+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+120+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+120+=+-16t%5E2+%2B+64t+%2B+8+ ALIGN=MIDDLE  ALT=\"+120+=+-16t%5E2+%2B+64t+%2B+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-16t%5E2+%2B+64t+-+112+=+0+ ALIGN=MIDDLE  ALT=\"+-16t%5E2+%2B+64t+-+112+=+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%5E2+%2B+4t+-+7+=+0+ ALIGN=MIDDLE  ALT=\"+-t%5E2+%2B+4t+-+7+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I'll complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-t%5E2+%2B+4t+=+7+ ALIGN=MIDDLE  ALT=\"+-t%5E2+%2B+4t+=+7+\"   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+-+4t+=+-7%0D%0A%7B%7B%7B+t%5E2+-+4t+%2B+%284%2F2%29%5E2+=+-7+%2B+%284%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+4t+=+-7%0D%0A%7B%7B%7B+t%5E2+-+4t+%2B+%284%2F2%29%5E2+=+-7+%2B+%284%2F2%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=+t%5E2+-+4t+%2B+4+=+-3+ ALIGN=MIDDLE  ALT=\"+t%5E2+-+4t+%2B+4+=+-3+\"   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+-+2+%29%5E2+=+-3+ ALIGN=MIDDLE  ALT=\"+%28+t+-+2+%29%5E2+=+-3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Both sides need to be a perfect square for this<BR>\n" );
document.write( "to work, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is not a square of anything.<BR>\n" );
document.write( "I don't think the object ever reaches 120 ft<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+6%2C+-10%2C+100%2C+-16x%5E2+%2B+64x+%2B+8+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+100%2C+-16x%5E2+%2B+64x+%2B+8+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It looks like it's maximum height is 72 ft at 2 sec<BR>\n" );
document.write( "Is something copied wrong?<BR>\n" );
document.write( "=============================<BR>\n" );
document.write( "Note:  it's = it is\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );