document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906686>Question 906686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function h(t) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++-16t%5E2+%2B+144t+%2B+576+ ALIGN=MIDDLE  ALT=\"++-16t%5E2+%2B+144t+%2B+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  gives the height (in feet) of a rock t seconds after it has been thrown upward. Draw the graph of h. Determine the maximum height of the rock and the time that it takes the rock to reach that maximum height. How do you know that there is a maximum height? Justify your answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #550022 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=550022\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "this is a parabola that opens downward and its vertex is max point\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+950%2C-16x%5E2+%2B+144x+%2B+576+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+950%2C-16x%5E2+%2B+144x+%2B+576+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "find coordinates of vertex:\r<BR>\n" );
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document.write( "t or x-coordinate: <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;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-144%2F2%28-16%29=-144%2F-32=4.5 ALIGN=MIDDLE  ALT=\"t=-144%2F2%28-16%29=-144%2F-32=4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "plug it in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+ ALIGN=MIDDLE  ALT=\"+h%28t%29+=+-16t%5E2+%2B+144t+%2B+576+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and find h or y-coordinate\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%284.5%29+=+-16%284.5%29%5E2+%2B+144%2A4.5+%2B+576+ ALIGN=MIDDLE  ALT=\"+h%284.5%29+=+-16%284.5%29%5E2+%2B+144%2A4.5+%2B+576+\"   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=+h%284.5%29+=+-16%2820.25%29+%2B+648+%2B+576+ ALIGN=MIDDLE  ALT=\"+h%284.5%29+=+-16%2820.25%29+%2B+648+%2B+576+\"   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=+h%284.5%29+=+-324+%2B+1224+ ALIGN=MIDDLE  ALT=\"+h%284.5%29+=+-324+%2B+1224+\"   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=+h%284.5%29+=+900+ ALIGN=MIDDLE  ALT=\"+h%284.5%29+=+900+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so, vertex is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >)= ( <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5 ALIGN=MIDDLE  ALT=\"4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900 ALIGN=MIDDLE  ALT=\"900\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the maximum \r<BR>\n" );
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document.write( "height of the rock is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=900 ALIGN=MIDDLE  ALT=\"h=900\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the time that it takes the rock to reach that maximum height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.5s ALIGN=MIDDLE  ALT=\"4.5s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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