document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926546>Question 926546</A>: <I><SPAN STYLE=\"word-break: break-all;\"> y=-16x^2+44x+30 represents the height of an object (in feet) that is fired up from an initial height and then lands on the ground some time (in seconds) later.<BR>\n" );
document.write( "a) From what height was the object launched?<BR>\n" );
document.write( "b) How high will the object reach? At what time will this occur?<BR>\n" );
document.write( "c) For how many seconds will the object be in the air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562319 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=562319\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+-16x%5E2+%2B+44x+%2B+30+ ALIGN=MIDDLE  ALT=\"+y+=+-16x%5E2+%2B+44x+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+ ALIGN=MIDDLE  ALT=\"+y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is feet and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is seconds,<BR>\n" );
document.write( "The object is fired up at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+0+ ALIGN=MIDDLE  ALT=\"+x+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so<BR>\n" );
document.write( "the initial height is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%280%29+=+-16x%5E2+%2B+44%2A0+%2B+30+ ALIGN=MIDDLE  ALT=\"+y%280%29+=+-16x%5E2+%2B+44%2A0+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%280%29+=+30+ ALIGN=MIDDLE  ALT=\"+y%280%29+=+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(a) 30 ft<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "When the form of the equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+ ALIGN=MIDDLE  ALT=\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the time of the<BR>\n" );
document.write( "maximum height is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-b%2F%282a%29+=+-44%2F%28+2%2A%28-16%29%29+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+-44%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=+-b%2F%282a%29+=+11%2F8+ ALIGN=MIDDLE  ALT=\"+-b%2F%282a%29+=+11%2F8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "To find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-16%2A%2811%2F8%29%5E2+%2B+44%2A%2811%2F8%29+%2B+30+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-16%2A%2811%2F8%29%5E2+%2B+44%2A%2811%2F8%29+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-16%2A%28+121%2F64+%29+%2B+121%2F2+%2B+30+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-16%2A%28+121%2F64+%29+%2B+121%2F2+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-30.25+%2B+60.5+%2B+30+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-30.25+%2B+60.5+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+60.25+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+60.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(b) 60.25 ft<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "The object is in the air until it hits the ground when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+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+=+-16x%5E2+%2B+44x+%2B+30+ ALIGN=MIDDLE  ALT=\"+0+=+-16x%5E2+%2B+44x+%2B+30+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-8x%5E2+%2B+22x+%2B+15+=+0+ ALIGN=MIDDLE  ALT=\"+-8x%5E2+%2B+22x+%2B+15+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------<BR>\n" );
document.write( "use quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-22+%2B-+sqrt%28+22%5E2+-+4%2A%28-8%29%2A15+%29%29+%2F+%282%2A%28-8%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-22+%2B-+sqrt%28+22%5E2+-+4%2A%28-8%29%2A15+%29%29+%2F+%282%2A%28-8%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=+x+=+%28-22+%2B-+sqrt%28+484+%2B+480%29%29+%2F+%28-16%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-22+%2B-+sqrt%28+484+%2B+480%29%29+%2F+%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-22+%2B+sqrt%28+964+%29+%29+%2F+%28-16%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-22+%2B+sqrt%28+964+%29+%29+%2F+%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28+-22+-+31.048+%29+%2F+%28-16%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-22+-+31.048+%29+%2F+%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-53.048+%2F+%28-16%29+ ALIGN=MIDDLE  ALT=\"+x+=+-53.048+%2F+%28-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3.3155+ ALIGN=MIDDLE  ALT=\"+x+=+3.3155+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(c) 3.3155 sec<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "check:<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+-1%2C+5%2C+-10%2C+70%2C+-16x%5E2+%2B+44x+%2B+30+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-1%2C+5%2C+-10%2C+70%2C+-16x%5E2+%2B+44x+%2B+30+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );