document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=906061>Question 906061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A ball is thrown across a playing field. Its path is given by the equation y = &#8722;0.005 x^2 + x + 6 , where x is the distance the ball has traveled horizontally, and y is its height above ground level, both measured in feet.\r<BR>\n" );
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document.write( "(a) What is the maximum height attained by the ball?<BR>\n" );
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document.write( "(b) How far has it traveled horizontally when it hits the ground? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #549622 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=549622\">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+=+-.005%2A+x%5E2+%2B+x+%2B+6+ ALIGN=MIDDLE  ALT=\"+y+=+-.005%2A+x%5E2+%2B+x+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The x-coordinate of the vertex is located at<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-b%2F%282a%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-b%2F%282a%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-1+%2F+%28+2%2A%28-.005%29+%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-1+%2F+%28+2%2A%28-.005%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+1%2F.01+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+1%2F.01+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+100+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-.005%2A+100%5E2+%2B+100+%2B+6+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-.005%2A+100%5E2+%2B+100+%2B+6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-50+%2B+106+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-50+%2B+106+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+56+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+56+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "The max height is 56 ft<BR>\n" );
document.write( "(b)<BR>\n" );
document.write( "It hits the ground when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+0+ ALIGN=MIDDLE  ALT=\"+y+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-.005%2A+x%5E2+%2B+x+%2B+6+=+0+ ALIGN=MIDDLE  ALT=\"+-.005%2A+x%5E2+%2B+x+%2B+6+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-200+ ALIGN=MIDDLE  ALT=\"+-200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+200x+-+1200+=+0+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+200x+-+1200+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+200x+=+1200+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+200x+=+1200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+200x+%2B+%28+200%2F2+%29%5E2+=+1200+%2B+%28+200%2F2+%29%5E2+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+200x+%2B+%28+200%2F2+%29%5E2+=+1200+%2B+%28+200%2F2+%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+-+200x+%2B+10000+=+11200+ ALIGN=MIDDLE  ALT=\"+x%5E2+-+200x+%2B+10000+=+11200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+x+-+100+%29%5E2+=+11200+ ALIGN=MIDDLE  ALT=\"+%28+x+-+100+%29%5E2+=+11200+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x++-+100+=+105.83+ ALIGN=MIDDLE  ALT=\"+x++-+100+=+105.83+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+205.83+ ALIGN=MIDDLE  ALT=\"+x+=+205.83+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When it hits the ground, it has traveled 205.83 ft<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Here's the plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+220%2C+-5%2C+60%2C+-.005%2Ax%5E2+%2B+x+%2B+6+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+220%2C+-5%2C+60%2C+-.005%2Ax%5E2+%2B+x+%2B+6+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );