document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=805928>Question 805928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The path of a diver is given by the following, where y is the height (in feet) and x is the horizontal distance from the end of the diving board (in feet).<BR>\n" );
document.write( "y=-4/9 x^2 + 24/9 x + 11<BR>\n" );
document.write( "What is the maximum height of the diver? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #485605 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=485605\">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=y=-%284%2F9%29+x%5E2+%2B+%2824%2F9%29+x+%2B+11 ALIGN=MIDDLE  ALT=\"y=-%284%2F9%29+x%5E2+%2B+%2824%2F9%29+x+%2B+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >..here you have parabola opened upside-down and maximum is at vertex; so, find coordinates of vertex\r<BR>\n" );
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document.write( "<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;\" > will give us the x-coordinate of the vertex: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=%2824%2F9%29 ALIGN=MIDDLE  ALT=\"b=%2824%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-%284%2F9%29 ALIGN=MIDDLE  ALT=\"a=-%284%2F9%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=x=-%2824%2F9%29%2F2%28-%284%2F9%29%29 ALIGN=MIDDLE  ALT=\"x=-%2824%2F9%29%2F2%28-%284%2F9%29%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=x=%28-24%2F9%29%2F%28-8%2F9%29 ALIGN=MIDDLE  ALT=\"x=%28-24%2F9%29%2F%28-8%2F9%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=x=%28-24%2A9%29%2F%28-8%2A9%29 ALIGN=MIDDLE  ALT=\"x=%28-24%2A9%29%2F%28-8%2A9%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=x=-24%2F-8 ALIGN=MIDDLE  ALT=\"x=-24%2F-8\"   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=x=3 ALIGN=MIDDLE  ALT=\"x=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now plug it in equation and find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   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=y=-%284%2F9%293%5E2+%2B+%2824%2F9%29+3+%2B+11 ALIGN=MIDDLE  ALT=\"y=-%284%2F9%293%5E2+%2B+%2824%2F9%29+3+%2B+11\"   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=y=-%284%2Fcross%289%29%29cross%289%29+%2B+%2824%2Fcross%289%293%29+cross%283%29+%2B+11 ALIGN=MIDDLE  ALT=\"y=-%284%2Fcross%289%29%29cross%289%29+%2B+%2824%2Fcross%289%293%29+cross%283%29+%2B+11\"   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=y=-4%2B+24%2F3++%2B+11 ALIGN=MIDDLE  ALT=\"y=-4%2B+24%2F3++%2B+11\"   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=y=-4%2B+8++%2B+11 ALIGN=MIDDLE  ALT=\"y=-4%2B+8++%2B+11\"   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=y=4++%2B+11 ALIGN=MIDDLE  ALT=\"y=4++%2B+11\"   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=y=15 ALIGN=MIDDLE  ALT=\"y=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "so,  the vertex is at:  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3 ALIGN=MIDDLE  ALT=\"+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "since given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+ ALIGN=MIDDLE  ALT=\"y+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the maximum height of the diver, it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+15ft ALIGN=MIDDLE  ALT=\"+15ft\"   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=+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+20%2C-%284%2F9%29+x%5E2+%2B+%2824%2F9%29+x+%2B+11%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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