document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286500>Question 286500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A model rocket is projected straight upward from the ground level according to the height equation               h= -16t^2+192t, where t is greater than or = to 0. What is the maximum height of the rocket and after how many seconds does the rocket reach maximum height?\r<BR>\n" );
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document.write( "I am just somewhat frustrated because it seems as thought the book and my lecture do not have sufficient information to answer this question, and I could really use some help. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207790 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=207790\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Note: I'm using 'x' instead of 't' and 'y' instead of 'h'\r<BR>\n" );
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document.write( "The max height will occur at the vertex since the vertex is the highest/lowest point on the parabola. So we must find the vertex.\r<BR>\n" );
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document.write( "To find the vertex, we'll use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the x coordinate of the vertex. Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-16x%5E2%2B192x ALIGN=MIDDLE  ALT=\"y=-16x%5E2%2B192x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is in the form <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;\" > 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=192 ALIGN=MIDDLE  ALT=\"b=192\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can plug these values in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a ALIGN=MIDDLE  ALT=\"x=-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-b%2F2a=-192%2F%282%28-16%29%29=-192%2F%28-32%29=6 ALIGN=MIDDLE  ALT=\"x=-b%2F2a=-192%2F%282%28-16%29%29=-192%2F%28-32%29=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the 'x' coordinate of the vertex is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So the highest point occurs when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=6 ALIGN=MIDDLE  ALT=\"x=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or equivalently when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since I replaced 't' with 'x'). So the rocket reaches the max height at 6 seconds.\r<BR>\n" );
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document.write( "From here, just plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=6 ALIGN=MIDDLE  ALT=\"t=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=-16t%5E2%2B192t ALIGN=MIDDLE  ALT=\"h=-16t%5E2%2B192t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find the height 'h' at that given 't' value. \r<BR>\n" );
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document.write( "Note: the vertex will be (6, h) where 'h' is the height at 6 seconds, but you probably don't need this info.  </SPAN>\n" );
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