document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=316805>Question 316805</A>: <I><SPAN STYLE=\"word-break: break-all;\"> h= -16t2 +80t + 50<BR>\n" );
document.write( "Use this position polynomial to calculate the following: \r<BR>\n" );
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document.write( "1.The height of the object after 2 seconds <BR>\n" );
document.write( "2.The height of the object after 5 seconds <BR>\n" );
document.write( "3.The maximum height of the object <BR>\n" );
document.write( "4.How long the the object will take to reach 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 #226797 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=226797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> h= -16t2 +80t + 50<BR>\n" );
document.write( "Use this position polynomial to calculate the following: <BR>\n" );
document.write( "1.The height of the object after 2 seconds <BR>\n" );
document.write( "h= -16(2)^2 +80(2) + 50<BR>\n" );
document.write( "h= -16(4) +160 + 50<BR>\n" );
document.write( "h= -64 +160 + 50<BR>\n" );
document.write( "h = 146 <BR>\n" );
document.write( "2.The height of the object after 5 seconds <BR>\n" );
document.write( "h= -16(5)^2 +80(5) + 50<BR>\n" );
document.write( "h= -16(25) +400 + 50<BR>\n" );
document.write( "h= 50<BR>\n" );
document.write( "3.The maximum height of the object <BR>\n" );
document.write( "axis of symmetry:<BR>\n" );
document.write( "t = -b/(2a) = -80/(-32) = 2.5<BR>\n" );
document.write( "h= -16(2.5)^2 +80(2.5) + 50<BR>\n" );
document.write( "h = 150<BR>\n" );
document.write( "4.How long the the object will take to reach the ground? <BR>\n" );
document.write( "set h to zero solve for t<BR>\n" );
document.write( "0= -16t2 +80t + 50<BR>\n" );
document.write( "Apply the quadratic formula to get:<BR>\n" );
document.write( "t = {-0.562, 5.562}<BR>\n" );
document.write( "Toss out the negative solution leaving:<BR>\n" );
document.write( "t = 5.562<BR>\n" );
document.write( "Details of quadratic to follow:<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=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=-16t%5E2%2B80t%2B50+=+0 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B80t%2B50+=+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=%2880%29%5E2-4%2A-16%2A50=9600 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2880%29%5E2-4%2A-16%2A50=9600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=9600 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+=+%28-80%2B-sqrt%28+9600+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-80%2B-sqrt%28+9600+%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-%2880%29%2Bsqrt%28+9600+%29%29%2F2%5C-16+=+-0.561862178478973 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+%28-%2880%29%2Bsqrt%28+9600+%29%29%2F2%5C-16+=+-0.561862178478973\"   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-%2880%29-sqrt%28+9600+%29%29%2F2%5C-16+=+5.56186217847897 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+%28-%2880%29-sqrt%28+9600+%29%29%2F2%5C-16+=+5.56186217847897\"   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=-16t%5E2%2B80t%2B50 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B80t%2B50\"   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=-16t%5E2%2B80t%2B50+=+-16%28t--0.561862178478973%29%2A%28t-5.56186217847897%29 ALIGN=MIDDLE  ALT=\"-16t%5E2%2B80t%2B50+=+-16%28t--0.561862178478973%29%2A%28t-5.56186217847897%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: -0.561862178478973, 5.56186217847897.\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%2B80%2Ax%2B50+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B80%2Ax%2B50+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );