document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200805>Question 1200805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height h metres of a ball at time t second after it is thrown up into the air Is given by the expression <BR>\n" );
document.write( "h= 1+ 15t - 5t^2<BR>\n" );
document.write( "(i) Find the times at which the height is 11m<BR>\n" );
document.write( "(ii) Use your calculator to find the time when the ball hits the ground<BR>\n" );
document.write( "(iii) what is the greatest height the ball reaches  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835016 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=835016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height h metres of a ball at time t second after it is thrown up into the air Is given by the expression <BR>\n" );
document.write( "h= 1+ 15t - 5t^2<BR>\n" );
document.write( "(i) Find the times at which the height is 11m<BR>\n" );
document.write( "h= 1+ 15t - 5t^2 = 11<BR>\n" );
document.write( "5t^2 - 15t + 10 = 0<BR>\n" );
document.write( "t^2 - 3t + 2 = 0<BR>\n" );
document.write( "(t-1)*(t-2) = 0<BR>\n" );
document.write( "t = 1, t = 2 seconds.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "(ii) Use your calculator to find the time when the ball hits the ground<BR>\n" );
document.write( "h= 1+ 15t - 5t^2 = 0\r<BR>\n" );
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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=-5x%5E2%2B15x%2B1+=+0 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B15x%2B1+=+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=%2815%29%5E2-4%2A-5%2A1=245 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2815%29%5E2-4%2A-5%2A1=245\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=245 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+=+%28-15%2B-sqrt%28+245+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-15%2B-sqrt%28+245+%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-%2815%29%2Bsqrt%28+245+%29%29%2F2%5C-5+=+-0.0652475842498529 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2815%29%2Bsqrt%28+245+%29%29%2F2%5C-5+=+-0.0652475842498529\"   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-%2815%29-sqrt%28+245+%29%29%2F2%5C-5+=+3.06524758424985 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2815%29-sqrt%28+245+%29%29%2F2%5C-5+=+3.06524758424985\"   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=-5x%5E2%2B15x%2B1 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B15x%2B1\"   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=-5x%5E2%2B15x%2B1+=+%28x--0.0652475842498529%29%2A%28x-3.06524758424985%29 ALIGN=MIDDLE  ALT=\"-5x%5E2%2B15x%2B1+=+%28x--0.0652475842498529%29%2A%28x-3.06524758424985%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.0652475842498529, 3.06524758424985.\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+-5%2Ax%5E2%2B15%2Ax%2B1+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B15%2Ax%2B1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "Ignore the negative value.<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "(iii) what is the greatest height the ball reaches<BR>\n" );
document.write( "The vertex of the parabola is at t = -b/2a<BR>\n" );
document.write( "t = -15/-10 = 1.5 seconds<BR>\n" );
document.write( "h(1.5) = 12.25 meters </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );