document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992194>Question 992194</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation\r<BR>\n" );
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document.write( " h = -16 t^2 + 160 t + 270\r<BR>\n" );
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document.write( "models the ball's height \, h \, above the ground in feet, t seconds after it was thrown.\r<BR>\n" );
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document.write( "How high is the ball after 5 seconds?\r<BR>\n" );
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document.write( "How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611819 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=611819\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person standing close to the edge on the top of a 270-foot building throws a baseball vertically upward. The quadratic equation <BR>\n" );
document.write( " h = -16 t^2 + 160 t + 270 <BR>\n" );
document.write( " models the ball's height h above the ground in feet, t seconds after it was thrown. <BR>\n" );
document.write( " How high is the ball after 5 seconds? <BR>\n" );
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document.write( "h(t) = -16t^2 + 160t + 270<BR>\n" );
document.write( "Find h(5) = sub 5 for t.<BR>\n" );
document.write( "h(5) is 670 feet.<BR>\n" );
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document.write( " How many seconds does it take until the ball finally hits the ground? Round to the nearest tenth of a second.<BR>\n" );
document.write( "h(t) = -16t^2 + 160t + 270<BR>\n" );
document.write( "-16t^2 + 160t + 270 = 0<BR>\n" );
document.write( "Solve for t.  Use the positive solution.<BR>\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%2B160x%2B270+=+0 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B160x%2B270+=+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=%28160%29%5E2-4%2A-16%2A270=42880 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28160%29%5E2-4%2A-16%2A270=42880\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=42880 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+=+%28-160%2B-sqrt%28+42880+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-160%2B-sqrt%28+42880+%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-%28160%29%2Bsqrt%28+42880+%29%29%2F2%5C-16+=+-1.47108955277239 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28160%29%2Bsqrt%28+42880+%29%29%2F2%5C-16+=+-1.47108955277239\"   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-%28160%29-sqrt%28+42880+%29%29%2F2%5C-16+=+11.4710895527724 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28160%29-sqrt%28+42880+%29%29%2F2%5C-16+=+11.4710895527724\"   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%2B160x%2B270 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B160x%2B270\"   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%2B160x%2B270+=+%28x--1.47108955277239%29%2A%28x-11.4710895527724%29 ALIGN=MIDDLE  ALT=\"-16x%5E2%2B160x%2B270+=+%28x--1.47108955277239%29%2A%28x-11.4710895527724%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -1.47108955277239, 11.4710895527724.\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%2B160%2Ax%2B270+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B160%2Ax%2B270+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t = 11.5 seconds.<BR>\n" );
document.write( "Maybe you didn't use the nearest 10th ? </SPAN>\n" );
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