document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1049249>Question 1049249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Herman arranged a game of water balloon volleyball for his daughter’s birthday party. Suppose the balloon has a height of h metres, t seconds after it is tossed, as defined by h = -5t^2 + 12t + 1.<BR>\n" );
document.write( "a) Write an equation that shows how many seconds will pass before the balloon hits the ground. Solve this equation,rounded to the nearest hundredth of a second.<BR>\n" );
document.write( "b) what is the maximum height reached by the balloon? When does it reach this height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664811 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=664811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (a)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-5t%5E2+%2B+12t+%2B+1+ ALIGN=MIDDLE  ALT=\"+h+=+-5t%5E2+%2B+12t+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "The ball is tossed at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+0+ ALIGN=MIDDLE  ALT=\"+t+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This gives you:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+-5%2A0%5E2+%2B+12%2A0+%2B+1+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+-5%2A0%5E2+%2B+12%2A0+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%280%29+=+1+ ALIGN=MIDDLE  ALT=\"+h%280%29+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They are saying that the ball is tossed from a height<BR>\n" );
document.write( "of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > meter<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "You want to know the time in seconds when<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+0+ ALIGN=MIDDLE  ALT=\"+h+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( balloon hits the ground )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5t%5E2+%2B+12t+%2B+1+=+0+ ALIGN=MIDDLE  ALT=\"+-5t%5E2+%2B+12t+%2B+1+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%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=+a+=+-5+ ALIGN=MIDDLE  ALT=\"+a+=+-5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+12+ ALIGN=MIDDLE  ALT=\"+b+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+1+ ALIGN=MIDDLE  ALT=\"+c+=+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+-12+%2B-+sqrt%28+12%5E2-4%2A%28-5%29%2A1+%29%29%2F%282%2A%28-5%29%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-12+%2B-+sqrt%28+12%5E2-4%2A%28-5%29%2A1+%29%29%2F%282%2A%28-5%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+=+%28+-12+%2B-+sqrt%28+144+%2B+20+%29%29%2F%28-10%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-12+%2B-+sqrt%28+144+%2B+20+%29%29%2F%28-10%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+=+%28+-12+%2B-+sqrt%28+164+%29%29%2F%28-10%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-12+%2B-+sqrt%28+164+%29%29%2F%28-10%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+=+%28+-12+-+12.8062+%29+%2F+%28-10%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28+-12+-+12.8062+%29+%2F+%28-10%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( time has to come out positive )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+24.8062+%2F+10+ ALIGN=MIDDLE  ALT=\"+t+=+24.8062+%2F+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2.4806+ ALIGN=MIDDLE  ALT=\"+t+=+2.4806+\"   DISABLED_style= \"max-width:90%; height:auto;\" > sec<BR>\n" );
document.write( "The balloon hits the ground in 2.48 sec<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-value at the maximum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+t%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=+t%5Bmax%5D+=+-12%2F%28+2%2A%28-5%29%29+ ALIGN=MIDDLE  ALT=\"+t%5Bmax%5D+=+-12%2F%28+2%2A%28-5%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%5Bmax%5D+=+1.2+ ALIGN=MIDDLE  ALT=\"+t%5Bmax%5D+=+1.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this value back into equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+ ALIGN=MIDDLE  ALT=\"+h%28t%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+-5t%5E2+%2B+12t+%2B+1+ ALIGN=MIDDLE  ALT=\"+h+=+-5t%5E2+%2B+12t+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.2%29+=+-5%2A1.2%5E2+%2B+12%2A1.2+%2B+1+ ALIGN=MIDDLE  ALT=\"+h%281.2%29+=+-5%2A1.2%5E2+%2B+12%2A1.2+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.2%29+=+-5%2A1.44+%2B+14.4+%2B+1+ ALIGN=MIDDLE  ALT=\"+h%281.2%29+=+-5%2A1.44+%2B+14.4+%2B+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.2%29+=+-7.2+%2B+15.4+ ALIGN=MIDDLE  ALT=\"+h%281.2%29+=+-7.2+%2B+15.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%281.2%29+=+8.2+ ALIGN=MIDDLE  ALT=\"+h%281.2%29+=+8.2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The maximm height is 8.2 m which it will<BR>\n" );
document.write( "reach in 1.2 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+-4%2C+4%2C+-4%2C+10%2C+-5x%5E2+%2B+12x+%2B+1+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+10%2C+-5x%5E2+%2B+12x+%2B+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "My numbers look pretty close\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );