document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211479>Question 211479</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0136007317/algebrahomeworkh>Beginning & Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> An object is thrown upward from the top of an 80 foot building with an initial velocity of 64 feet per second. The height h of an object after t seconds is given by the quadratic equation (((h=-16t^2+64t+80))). When will the object hit 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 #159818 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=159818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem gives you:<BR>\n" );
document.write( "h=-16t^2+64t+80<BR>\n" );
document.write( "where<BR>\n" );
document.write( "h is height in feet<BR>\n" );
document.write( "t is time in secs<BR>\n" );
document.write( ".<BR>\n" );
document.write( "If it hits the ground, h = 0 so <BR>\n" );
document.write( "set h=0 and solve for t:<BR>\n" );
document.write( "h=-16t^2+64t+80<BR>\n" );
document.write( "0=-16t^2+64t+80<BR>\n" );
document.write( "0=-4t^2+16t+5<BR>\n" );
document.write( "Solving using the quadratic equation yields:<BR>\n" );
document.write( "t = {-0.29, 4.29}<BR>\n" );
document.write( "We can throw out the negative solution leaving<BR>\n" );
document.write( "t = 4.29 seconds<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic to follow:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=at%5E2%2Bbt%2Bc=0 ALIGN=MIDDLE  ALT=\"at%5E2%2Bbt%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4t%5E2%2B16t%2B5+=+0 ALIGN=MIDDLE  ALT=\"-4t%5E2%2B16t%2B5+=+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=t%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"t%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=%2816%29%5E2-4%2A-4%2A5=336 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2816%29%5E2-4%2A-4%2A5=336\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=336 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+=+%28-16%2B-sqrt%28+336+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-16%2B-sqrt%28+336+%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=t%5B1%5D+=+%28-%2816%29%2Bsqrt%28+336+%29%29%2F2%5C-4+=+-0.29128784747792 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2816%29%2Bsqrt%28+336+%29%29%2F2%5C-4+=+-0.29128784747792\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+%28-%2816%29-sqrt%28+336+%29%29%2F2%5C-4+=+4.29128784747792 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2816%29-sqrt%28+336+%29%29%2F2%5C-4+=+4.29128784747792\"   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=-4t%5E2%2B16t%2B5 ALIGN=MIDDLE  ALT=\"-4t%5E2%2B16t%2B5\"   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=-4t%5E2%2B16t%2B5+=+-4%28t--0.29128784747792%29%2A%28t-4.29128784747792%29 ALIGN=MIDDLE  ALT=\"-4t%5E2%2B16t%2B5+=+-4%28t--0.29128784747792%29%2A%28t-4.29128784747792%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.29128784747792, 4.29128784747792.\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+-4%2Ax%5E2%2B16%2Ax%2B5+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B16%2Ax%2B5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );