document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=215961>Question 215961</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780495013570/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The height of an object is given by h=-16t^2+v^0t+h^0 ft. after t seconds, where v^0 is the initial velocity of the object in ft./sec and h^0 is the initial height of the object in feet.\r<BR>\n" );
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document.write( "An object is thrown upwards from the top of a 650ft. building at an initial velocity of 64 ft./sec.\r<BR>\n" );
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document.write( "a) For what t>0 is the object feet from the ground?\r<BR>\n" );
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document.write( "b)For what t.0 is the object on 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 #163139 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=163139\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The height of an object is given by h=-16t^2+v^0t+h^0 ft. after t seconds, where v^0 is the initial velocity of the object in ft./sec and h^0 is the initial height of the object in feet. <BR>\n" );
document.write( "An object is thrown upwards from the top of a 650ft. building at an initial velocity of 64 ft./sec. <BR>\n" );
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document.write( "h(t) = -16t^2 + 64t + 650<BR>\n" );
document.write( "a) For what t>0 is the object feet from the ground?<BR>\n" );
document.write( "?? How many feet?<BR>\n" );
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document.write( "b)For what t.0 is the object on the ground?<BR>\n" );
document.write( "-16t^2 + 64t + 650 = 0<BR>\n" );
document.write( "-8t^2 + 32t + 325 = 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=-8x%5E2%2B32x%2B325+=+0 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B32x%2B325+=+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=%2832%29%5E2-4%2A-8%2A325=11424 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2832%29%5E2-4%2A-8%2A325=11424\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=11424 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+=+%28-32%2B-sqrt%28+11424+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-32%2B-sqrt%28+11424+%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-%2832%29%2Bsqrt%28+11424+%29%29%2F2%5C-8+=+-4.68019460794369 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+11424+%29%29%2F2%5C-8+=+-4.68019460794369\"   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-%2832%29-sqrt%28+11424+%29%29%2F2%5C-8+=+8.68019460794369 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2832%29-sqrt%28+11424+%29%29%2F2%5C-8+=+8.68019460794369\"   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=-8x%5E2%2B32x%2B325 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B32x%2B325\"   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=-8x%5E2%2B32x%2B325+=+%28x--4.68019460794369%29%2A%28x-8.68019460794369%29 ALIGN=MIDDLE  ALT=\"-8x%5E2%2B32x%2B325+=+%28x--4.68019460794369%29%2A%28x-8.68019460794369%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -4.68019460794369, 8.68019460794369.\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+-8%2Ax%5E2%2B32%2Ax%2B325+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B32%2Ax%2B325+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "t = ~ 8.68 seconds<BR>\n" );
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