document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147130>Question 147130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The path of the diver is given by y= 4/9 x^2+24/9 x+12<BR>\n" );
document.write( "where y is the height in feet and x is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?\r<BR>\n" );
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document.write( "Thank you for any help here. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107558 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107558\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The path of the diver is given by y= 4/9x^2 + 24/9x + 12<BR>\n" );
document.write( "where <BR>\n" );
document.write( "y is the height in feet<BR>\n" );
document.write( "x is the horizontal distance from the end of the diving board (in feet).<BR>\n" );
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document.write( "The coefficient of x^2 has to be negative to have a maximum, assuming the equation is:<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F9 ALIGN=MIDDLE  ALT=\"-4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F9 ALIGN=MIDDLE  ALT=\"24%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >x + 12<BR>\n" );
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document.write( "Find the axis of symmetry using the formula: x =-b/(2a); a=-4/9; b=24/9<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-24%2F9%29%2F%282%2A%28-4%2F9%29%29 ALIGN=MIDDLE  ALT=\"%28-24%2F9%29%2F%282%2A%28-4%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-24%2F9%29%2F%28%28-8%2F9%29%29 ALIGN=MIDDLE  ALT=\"%28-24%2F9%29%2F%28%28-8%2F9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Invert the dividing fraction and multiply<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-24%2F9%29%2A%28-9%2F8%29 ALIGN=MIDDLE  ALT=\"%28-24%2F9%29%2A%28-9%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cancel and you have:<BR>\n" );
document.write( "x = +3 ft horizontal distance from end of diving board for max height<BR>\n" );
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document.write( "What is the maximum height of the diver?<BR>\n" );
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document.write( "Substitute 3 for x in the original equation to find max height<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F9 ALIGN=MIDDLE  ALT=\"-4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >3^2 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2F9 ALIGN=MIDDLE  ALT=\"24%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >3 + 12<BR>\n" );
document.write( ":<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F9 ALIGN=MIDDLE  ALT=\"-4%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" >9 + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2F9 ALIGN=MIDDLE  ALT=\"72%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 12<BR>\n" );
document.write( "cancel<BR>\n" );
document.write( "y = -4 + 8 + 12<BR>\n" );
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document.write( "y = 16 ft is max height<BR>\n" );
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document.write( "A graph of this equation will make it clear:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+12%2C+-10%2C+20%2C+%28-4%2F9%29x%5E2%2B%2824%2F9%29x%2B12%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-6%2C+12%2C+-10%2C+20%2C+%28-4%2F9%29x%5E2%2B%2824%2F9%29x%2B12%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note this also shows the diving board to be 12 ft above the water and he will enter the water 9 ft from the end of the diving board.<BR>\n" );
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document.write( "Did this make some sense to you?<BR>\n" );
document.write( "  </SPAN>\n" );
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