document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=613244>Question 613244</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown off the top of a classroom building with an initial upward velocity of 10 feet per second. The height above the ground can be found using h= -16t(squared) + 10t + 40 with t representing time in seconds and h representing height in feet. How high is the ball after 0.8 seconds? When will the ball be 20 feet above the ground and headed down? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385906 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=385906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown off the top of a classroom building with an initial upward velocity of 10 feet per second. The height above the ground can be found using h= -16t(squared) + 10t + 40 with t representing time in seconds and h representing height in feet. How high is the ball after 0.8 seconds?<BR>\n" );
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document.write( "Sub 0.8 for t<BR>\n" );
document.write( "h(0.8) = -16*0.8^2 + 10*0.8 + 40<BR>\n" );
document.write( "= 37.76 feet<BR>\n" );
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document.write( "When will the ball be 20 feet above the ground and headed down?<BR>\n" );
document.write( "h = 20<BR>\n" );
document.write( "20 = -16t^2 + 10t + 40<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2+%2B+10t+%2B+20+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2+%2B+10t+%2B+20+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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=-16x%5E2%2B10x%2B20+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B10x%2B20+=+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=%2810%29%5E2-4%2A-16%2A20=1380 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2810%29%5E2-4%2A-16%2A20=1380\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1380 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+=+%28-10%2B-sqrt%28+1380+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-10%2B-sqrt%28+1380+%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-%2810%29%2Bsqrt%28+1380+%29%29%2F2%5C-16+=+-0.848385976312919 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+1380+%29%29%2F2%5C-16+=+-0.848385976312919\"   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-%2810%29-sqrt%28+1380+%29%29%2F2%5C-16+=+1.47338597631292 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2810%29-sqrt%28+1380+%29%29%2F2%5C-16+=+1.47338597631292\"   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=-16x%5E2%2B10x%2B20 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B10x%2B20\"   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=-16x%5E2%2B10x%2B20+=+%28x--0.848385976312919%29%2A%28x-1.47338597631292%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B10x%2B20+=+%28x--0.848385976312919%29%2A%28x-1.47338597631292%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.848385976312919, 1.47338597631292.\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+-16%2Ax%5E2%2B10%2Ax%2B20+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B10%2Ax%2B20+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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