document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=536600>Question 536600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person standing cloes to the edge on the top of a 200-foot building throws a baseball vertically upward. The quadratic function\r<BR>\n" );
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document.write( "                        s(t)=-16t^2+64t+200\r<BR>\n" );
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document.write( "models the ball's height above the ground, s(t), in feet, t seconds after it was thrown.<BR>\n" );
document.write( "A)After how many seconds does the ball reach it's maximum height? What is the maximum height?<BR>\n" );
document.write( "B)How many seconds does it take until the ball finally hits 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 #352454 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=352454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A person standing cloes to the edge on the top of a 200-foot building throws a baseball vertically upward. The quadratic function\r<BR>\n" );
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document.write( "                        s(t)=-16t^2+64t+200\r<BR>\n" );
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document.write( "models the ball's height above the ground, s(t), in feet, t seconds after it was thrown.<BR>\n" );
document.write( "A)After how many seconds does the ball reach it's [sic] maximum height? What is the maximum height?<BR>\n" );
document.write( "The equation is a parabola, the max height is at the vertex.<BR>\n" );
document.write( "The vertex is on the line of symmetry, which is<BR>\n" );
document.write( "t = -b/2a<BR>\n" );
document.write( "t = -64/-32 = 2 seconds<BR>\n" );
document.write( "s(2) = -16*4 + 64*2 + 200<BR>\n" );
document.write( "max ht = 264 ft<BR>\n" );
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document.write( "B)How many seconds does it take until the ball finally hits the ground?<BR>\n" );
document.write( "Find t when s(t) = 0<BR>\n" );
document.write( "-16t^2 + 64t + 200 = 0<BR>\n" );
document.write( "2t^2 - 8t - 25 = 0<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=2x%5E2%2B-8x%2B-25+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-8x%2B-25+=+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=%28-8%29%5E2-4%2A2%2A-25=264 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-8%29%5E2-4%2A2%2A-25=264\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=264 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--8%2B-sqrt%28+264+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--8%2B-sqrt%28+264+%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-%28-8%29%2Bsqrt%28+264+%29%29%2F2%5C2+=+6.06201920231798 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+264+%29%29%2F2%5C2+=+6.06201920231798\"   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-%28-8%29-sqrt%28+264+%29%29%2F2%5C2+=+-2.06201920231798 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-8%29-sqrt%28+264+%29%29%2F2%5C2+=+-2.06201920231798\"   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=2x%5E2%2B-8x%2B-25 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-8x%2B-25\"   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=2x%5E2%2B-8x%2B-25+=+%28x-6.06201920231798%29%2A%28x--2.06201920231798%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-8x%2B-25+=+%28x-6.06201920231798%29%2A%28x--2.06201920231798%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6.06201920231798, -2.06201920231798.\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%2B-8%2Ax%2B-25+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-8%2Ax%2B-25+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative solution<BR>\n" );
document.write( "t =~ 6.062 seconds<BR>\n" );
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document.write( "PS  it's = it is </SPAN>\n" );
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