document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200858>Question 200858</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073533490/algebrahomeworkh>Elementary and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Throwing a wrench. An angry construction worker throws<BR>\n" );
document.write( "his wrench downward from a height of 128 feet with an<BR>\n" );
document.write( "initial velocity of 32 feet per second. The height of the<BR>\n" );
document.write( "wrench above the ground after t seconds is given<BR>\n" );
document.write( "by S(t) = -16t2 - 32t + 128.<BR>\n" );
document.write( "a) What is the height of the wrench after 1 second?<BR>\n" );
document.write( "b) How long does it take for the wrench to reach the<BR>\n" );
document.write( "ground?<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 #151105 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=151105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29=-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29=-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29=-16%281%29%5E2-32%281%29%2B128 ALIGN=MIDDLE  ALT=\"S%281%29=-16%281%29%5E2-32%281%29%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29=-16%281%29-32%281%29%2B128 ALIGN=MIDDLE  ALT=\"S%281%29=-16%281%29-32%281%29%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29=-16-32%281%29%2B128 ALIGN=MIDDLE  ALT=\"S%281%29=-16-32%281%29%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29=-16-32%2B128 ALIGN=MIDDLE  ALT=\"S%281%29=-16-32%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%281%29=80 ALIGN=MIDDLE  ALT=\"S%281%29=80\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "So the wrench is 80 feet in the air after 1 second.\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29=-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"S%28t%29=-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given function.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"0=-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28t%29=0 ALIGN=MIDDLE  ALT=\"S%28t%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie make the height equal to zero).\r<BR>\n" );
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document.write( "Notice that the quadratic <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2-32t%2B128 ALIGN=MIDDLE  ALT=\"-16t%5E2-32t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=At%5E2%2BBt%2BC ALIGN=MIDDLE  ALT=\"At%5E2%2BBt%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-16 ALIGN=MIDDLE  ALT=\"A=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-32 ALIGN=MIDDLE  ALT=\"B=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=128 ALIGN=MIDDLE  ALT=\"C=128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for \"t\":\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 ALIGN=MIDDLE  ALT=\"t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-32%29+%2B-+sqrt%28+%28-32%29%5E2-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28-%28-32%29+%2B-+sqrt%28+%28-32%29%5E2-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=-16 ALIGN=MIDDLE  ALT=\"A=-16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=-32 ALIGN=MIDDLE  ALT=\"B=-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=128 ALIGN=MIDDLE  ALT=\"C=128\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+%28-32%29%5E2-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+%28-32%29%5E2-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32 ALIGN=MIDDLE  ALT=\"32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+1024-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+1024-4%28-16%29%28128%29+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+1024--8192+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+1024--8192+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28-16%29%28128%29 ALIGN=MIDDLE  ALT=\"4%28-16%29%28128%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8192 ALIGN=MIDDLE  ALT=\"-8192\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+1024%2B8192+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+1024%2B8192+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281024--8192%29 ALIGN=MIDDLE  ALT=\"sqrt%281024--8192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281024%2B8192%29 ALIGN=MIDDLE  ALT=\"sqrt%281024%2B8192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+9216+%29%29%2F%282%28-16%29%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+9216+%29%29%2F%282%28-16%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1024 ALIGN=MIDDLE  ALT=\"1024\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8192 ALIGN=MIDDLE  ALT=\"8192\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9216 ALIGN=MIDDLE  ALT=\"9216\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+sqrt%28+9216+%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+sqrt%28+9216+%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16 ALIGN=MIDDLE  ALT=\"-16\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-32 ALIGN=MIDDLE  ALT=\"-32\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B-+96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B-+96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9216 ALIGN=MIDDLE  ALT=\"9216\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=96 ALIGN=MIDDLE  ALT=\"96\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+%2B+96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+%2B+96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2832+-+96%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%2832+-+96%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28128%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=+%28128%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=++%28-64%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t+=++%28-64%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-4 ALIGN=MIDDLE  ALT=\"t+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the <i>possible</i> solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-4 ALIGN=MIDDLE  ALT=\"t+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "But remember that a negative time value doesn't make much sense. So we'll ignore <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-4 ALIGN=MIDDLE  ALT=\"t+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2 ALIGN=MIDDLE  ALT=\"t+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that it takes 2 seconds for the wrench to hit the ground.  </SPAN>\n" );
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