document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179599>Question 179599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rock is thrown from the top of a building. The distance is feet, between the rock and the ground \"t\" seconds after it is thrown is given by   d=16t^2+64X+128       <BR>\n" );
document.write( "what is the maximum height that the rock reaches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134521 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=134521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your problem statement seems to have some anomalies in it!<BR>\n" );
document.write( "The standard formula for the height (as a function of time) of an object propelled upwards from an initial height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D ALIGN=MIDDLE  ALT=\"h%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > with an initial velocity of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D ALIGN=MIDDLE  ALT=\"v%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > where g (the constant of acceleration due to gravity) is 32 ft/sec^2, so your formula should look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your formula also shows two different varaibles. t and x.<BR>\n" );
document.write( "So, back to the problem but starting with the correct formul, (the d in your problem will work just as well as the h(t)) we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+-16t%5E2%2B64t%2B128 ALIGN=MIDDLE  ALT=\"d+=+-16t%5E2%2B64t%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" > First, we'll find the time, t, at which the height, d, is at its maximum. The graph of the quadradtic equation that we have here is a parabola that opens downward (signified by the negative first term) so its maximum will occur at the vertex of the parabola, and this is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-b%2F2a ALIGN=MIDDLE  ALT=\"t+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where a = -16 and b = 64, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-%2864%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+-%2864%29%2F2%28-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >}<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+-64%2F-32 ALIGN=MIDDLE  ALT=\"t+=+-64%2F-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<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;\" >secs.<BR>\n" );
document.write( "To find the maximum height, we substitute the time, t=2secs into the original equation and solve for d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+-16%282%29%5E2%2B64%282%29%2B128 ALIGN=MIDDLE  ALT=\"d+=+-16%282%29%5E2%2B64%282%29%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+-16%284%29%2B128%2B128 ALIGN=MIDDLE  ALT=\"d+=+-16%284%29%2B128%2B128\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+-64%2B256 ALIGN=MIDDLE  ALT=\"d+=+-64%2B256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d+=+192%29 ALIGN=MIDDLE  ALT=\"highlight%28d+=+192%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet. <BR>\n" );
document.write( "The rock will reach a maximum height of 192 feet. </SPAN>\n" );
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