document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=337633>Question 337633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air.  The height in feet h(t) of the ball at t seconds is given by the formula<BR>\n" );
document.write( "H(t) = -16t^2 + 96t +56<BR>\n" );
document.write( "a)How tall is the building (hint: t=0)<BR>\n" );
document.write( "b)When is the ball at its highest point?<BR>\n" );
document.write( "c)To what height does the ball travel?<BR>\n" );
document.write( "d)When does the ball strike 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 #242080 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=242080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula<BR>\n" );
document.write( "H(t) = -16t^2 + 96t +56<BR>\n" );
document.write( "a)How tall is the building (hint: t=0)<BR>\n" );
document.write( "H(t) = -16t^2 + 96t +56<BR>\n" );
document.write( "H(0) = -16(0)^2 + 96(0) +56<BR>\n" );
document.write( "H(0) = 0 + 0 +56<BR>\n" );
document.write( "H(0) = 56 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b)When is the ball at its highest point?<BR>\n" );
document.write( "find the \"axis of symmetry\":<BR>\n" );
document.write( "t = -b/(2a) = -96/(2*(-16)) = -96/(-32) = 3 secs<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c)To what height does the ball travel?<BR>\n" );
document.write( "set t=3:<BR>\n" );
document.write( "H(t) = -16t^2 + 96t +56<BR>\n" );
document.write( "H(3) = -16(3)^2 + 96(3) +56<BR>\n" );
document.write( "H(3) = -16(9) + 96(3) +56<BR>\n" );
document.write( "H(3) = -144 + 288 +56<BR>\n" );
document.write( "H(3) = 200 feet<BR>\n" );
document.write( ".<BR>\n" );
document.write( "d)When does the ball strike the ground?<BR>\n" );
document.write( "Set H(t)=0 and solve for t:<BR>\n" );
document.write( "H(t) = -16t^2 + 96t +56<BR>\n" );
document.write( "0 = -16t^2 + 96t +56<BR>\n" );
document.write( "Dividing both sides by 8:<BR>\n" );
document.write( "0 = -2t^2 + 12t + 7<BR>\n" );
document.write( "Apply quadratic formula to get:<BR>\n" );
document.write( "t = {-0.54, 6.54}<BR>\n" );
document.write( "Toss out the negative solution to get<BR>\n" );
document.write( "t = 6.54 secs<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic follows:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%5E2%2B12t%2B7+=+0 ALIGN=MIDDLE  ALT=\"-2t%5E2%2B12t%2B7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2812%29%5E2-4%2A-2%2A7=200 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2812%29%5E2-4%2A-2%2A7=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=200 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-12%2B-sqrt%28+200+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-12%2B-sqrt%28+200+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+%28-%2812%29%2Bsqrt%28+200+%29%29%2F2%5C-2+=+-0.535533905932738 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2812%29%2Bsqrt%28+200+%29%29%2F2%5C-2+=+-0.535533905932738\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%2812%29-sqrt%28+200+%29%29%2F2%5C-2+=+6.53553390593274 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2812%29-sqrt%28+200+%29%29%2F2%5C-2+=+6.53553390593274\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%5E2%2B12t%2B7 ALIGN=MIDDLE  ALT=\"-2t%5E2%2B12t%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2t%5E2%2B12t%2B7+=+-2%28t--0.535533905932738%29%2A%28t-6.53553390593274%29 ALIGN=MIDDLE  ALT=\"-2t%5E2%2B12t%2B7+=+-2%28t--0.535533905932738%29%2A%28t-6.53553390593274%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.535533905932738, 6.53553390593274.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B12%2Ax%2B7+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B12%2Ax%2B7+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );