document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150370>Question 150370</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0131953648/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help. If a rock is thrown upward with an initial velocity of 40 feet per second from the top of a 30 foot building how high is the rock after 2 seconds,how many seconds will the graph reach maximum height and what is the maximum height? Can someone please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110303 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=110303\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To start solving this type of problem, you should know that the height (h) of an object propelled upward from a 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;\" > from the earth's surface 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;\" >ft./sec. is given by the function:<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( "In this problem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5B0%5D+=+40 ALIGN=MIDDLE  ALT=\"v%5B0%5D+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft./sec. and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B0%5D+=+30 ALIGN=MIDDLE  ALT=\"h%5B0%5D+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft. and you want to find the height, h, when t = 2 secs., so, substitute t = 2 and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-16%282%29%5E2%2B40%282%29%2B30 ALIGN=MIDDLE  ALT=\"h%282%29+=+-16%282%29%5E2%2B40%282%29%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+-64%2B80%2B30 ALIGN=MIDDLE  ALT=\"h%282%29+=+-64%2B80%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%282%29+=+46 ALIGN=MIDDLE  ALT=\"h%282%29+=+46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1) The rock is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2846%29 ALIGN=MIDDLE  ALT=\"highlight%2846%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet high after 2 seconds.<BR>\n" );
document.write( "The maximum height can easily be found when you realize that this quadratic function, when graphed, represents a parabola that opens downwards (negative <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > coefficient), so you need to find the location of the vertex (maximum) of the parabola.<BR>\n" );
document.write( "The independent variable is t (time) so the t-coordinate of the vertex 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 the a and b come from the standard form of the quadratic equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so, in this problem,  a = -16 and b = 40<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-40%29%2F2%28-16%29 ALIGN=MIDDLE  ALT=\"t+=+%28-40%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+=+40%2F32 ALIGN=MIDDLE  ALT=\"t+=+40%2F32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1.25 ALIGN=MIDDLE  ALT=\"t+=+1.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >secs.<BR>\n" );
document.write( "The maximum height occurs at time <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t+=+1.25%29 ALIGN=MIDDLE  ALT=\"highlight%28t+=+1.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > seconds. Now substitute this value of t into the quadratic function to find the height of the rock at time t = 1.25.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281.25%29+=+-16%281.25%29%5E2%2B40%281.25%29%2B30 ALIGN=MIDDLE  ALT=\"h%281.25%29+=+-16%281.25%29%5E2%2B40%281.25%29%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%281.25%29+=+55 ALIGN=MIDDLE  ALT=\"h%281.25%29+=+55\"   DISABLED_style= \"max-width:90%; height:auto;\" >feet.<BR>\n" );
document.write( "The maximum height attained by the rock is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h+=+55%29 ALIGN=MIDDLE  ALT=\"highlight%28h+=+55%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > feet. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );