document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762872>Question 762872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At 9:45 am Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = –0.6t2 + 108t + 75. <BR>\n" );
document.write( "a.	What will be the maximum height of the ball? __________<BR>\n" );
document.write( "b.	How long will it take the ball reach its maximum height? __________<BR>\n" );
document.write( "c.	At what time will the ball hit the ground? _________<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #464352 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=464352\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: <BR>\n" );
document.write( "h(t) = –0.6t2 + 108t + 75.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "b.	How long will it take the ball reach its maximum height?<BR>\n" );
document.write( "The equation is of a parabola.<BR>\n" );
document.write( "The max ht is the vertex.<BR>\n" );
document.write( "The vertex is on the axis of symmetry, t = -b/2a<BR>\n" );
document.write( "t = -108/(2*-0.6) = 90 seconds<BR>\n" );
document.write( "==========<BR>\n" );
document.write( "a.	What will be the maximum height of the ball?<BR>\n" );
document.write( "Max ht = h(90)<BR>\n" );
document.write( "= -0.6*90^2 + 108*90 + 75<BR>\n" );
document.write( "= 4935 ft<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "c.	At what time will the ball hit the ground?<BR>\n" );
document.write( "When h(t) = 0<BR>\n" );
document.write( "h(t) = –0.6t^2 + 108t + 75 = 0<BR>\n" );
document.write( "6t^2 - 1080t - 750 = 0<BR>\n" );
document.write( "t^2 - 180t - 125 = 0<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-180x%2B-125+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-180x%2B-125+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-180%29%5E2-4%2A1%2A-125=32900 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-180%29%5E2-4%2A1%2A-125=32900\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=32900 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--180%2B-sqrt%28+32900+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--180%2B-sqrt%28+32900+%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=x%5B1%5D+=+%28-%28-180%29%2Bsqrt%28+32900+%29%29%2F2%5C1+=+180.691785736085 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-180%29%2Bsqrt%28+32900+%29%29%2F2%5C1+=+180.691785736085\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-180%29-sqrt%28+32900+%29%29%2F2%5C1+=+-0.691785736085265 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-180%29-sqrt%28+32900+%29%29%2F2%5C1+=+-0.691785736085265\"   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=1x%5E2%2B-180x%2B-125 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-180x%2B-125\"   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=1x%5E2%2B-180x%2B-125+=+%28x-180.691785736085%29%2A%28x--0.691785736085265%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-180x%2B-125+=+%28x-180.691785736085%29%2A%28x--0.691785736085265%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 180.691785736085, -0.691785736085265.\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+1%2Ax%5E2%2B-180%2Ax%2B-125+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-180%2Ax%2B-125+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "============<BR>\n" );
document.write( "t =~ 180.69 seconds<BR>\n" );
document.write( "Ignore the negative solution<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );