document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964089>Question 964089</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A frog jumps from a rock to the shore of a pond. Its path is given by the equation:y = -5/72x^2+5/3x  , where x is the horizontal distance in inches, and y is the height in inches. What is the frog’s maximum height? How far had it traveled horizontally when it reached its maximum height? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588970 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588970\">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=%28-5%2F72%29x%5E2%2B%285%2F3%29x ALIGN=MIDDLE  ALT=\"y=%28-5%2F72%29x%5E2%2B%285%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "By letting y=0, we can find the horizontal distance at the start (0 in traveled) and the end of the jump: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28-5%2F72%29x%5E2%2B%285%2F3%29x ALIGN=MIDDLE  ALT=\"0=%28-5%2F72%29x%5E2%2B%285%2F3%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%5E2-24x ALIGN=MIDDLE  ALT=\"0=x%5E2-24x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x-24 ALIGN=MIDDLE  ALT=\"0=x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24=x ALIGN=MIDDLE  ALT=\"24=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The frog traveled 24 inches to the shore.<BR>\n" );
document.write( "The maximum height would be mid way, when x=12 in, so<BR>\n" );
document.write( "ANSWER 1: Maximum height at 12 inches horizontal distance.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F72%29%2812in%29%5E2%2B%285%2F3%29%2812in%29 ALIGN=MIDDLE  ALT=\"y=%28-5%2F72%29%2812in%29%5E2%2B%285%2F3%29%2812in%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F72%29%28144%29%2B%2860%2F3%29 ALIGN=MIDDLE  ALT=\"y=%28-5%2F72%29%28144%29%2B%2860%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-10%29%2B%2820%29 ALIGN=MIDDLE  ALT=\"y=%28-10%29%2B%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10in ALIGN=MIDDLE  ALT=\"y=10in\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ANSWER 2: Maximum height was 10 inches.<BR>\n" );
document.write( "This graph is sort of a picture of the jump:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+800%2C+400%2C+0%2C+24%2C+0%2C+11%2C+%28-5%2F72%29x%5E2%2B%285%2F3%29x%29 ALIGN=MIDDLE  ALT=\"+graph%28+800%2C+400%2C+0%2C+24%2C+0%2C+11%2C+%28-5%2F72%29x%5E2%2B%285%2F3%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );