document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094800>Question 1094800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amy throws a ball so that when it is at its highest point, it passes through a hoop. The path of the ball is modelled by the equation y = h + kx - 0.5x^2<BR>\n" );
document.write( "where y is the height of the ball above the ground and x is the horizontal distance from the point at which the ball was thrown. The centre of the Hoop is at the point where x = 2 and y = 5 \r<BR>\n" );
document.write( "\n" );
document.write( "Find the values of h and k and find the value of x for when the ball hits the ground. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #709399 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=709399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The x-value of the maximum is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+-k%2F%282%2A%28-.5%29%29+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+-k%2F%282%2A%28-.5%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+=+k+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+k+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5Bmax%5D+=+-.5%2Ak%5E2+%2B+k%2Ak+%2B+h+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+-.5%2Ak%5E2+%2B+k%2Ak+%2B+h+\"   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+=+.5%2Ak%5E2+%2B+h+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+.5%2Ak%5E2+%2B+h+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "The maximum point is at ( 2,5 )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5Bmax%5D+=+2+ ALIGN=MIDDLE  ALT=\"+x%5Bmax%5D+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+k+=+2+ ALIGN=MIDDLE  ALT=\"+k+=+2+\"   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+=+5+ ALIGN=MIDDLE  ALT=\"+y%5Bmax%5D+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.5k%5E2+%2B+h+=+5+ ALIGN=MIDDLE  ALT=\"+.5k%5E2+%2B+h+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+.5%2A2%5E2+%2B+h+=+5+ ALIGN=MIDDLE  ALT=\"+.5%2A2%5E2+%2B+h+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+5+-+2+ ALIGN=MIDDLE  ALT=\"+h+=+5+-+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h+=+3+ ALIGN=MIDDLE  ALT=\"+h+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "The ball hits the ground at <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=+-.5x%5E2+%2B+2x+%2B+3+=+0+ ALIGN=MIDDLE  ALT=\"+-.5x%5E2+%2B+2x+%2B+3+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A%28-.5%29%2A3+%29%29%2F%282%2A%28-.5%29%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A%28-.5%29%2A3+%29%29%2F%282%2A%28-.5%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+=+%28+-2+-+sqrt%28+4+%2B+6+%29+%29+%2F+%28-1%29+ ALIGN=MIDDLE  ALT=\"+x+=+%28+-2+-+sqrt%28+4+%2B+6+%29+%29+%2F+%28-1%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+=+2+%2B+sqrt%2810%29+ ALIGN=MIDDLE  ALT=\"+x+=+2+%2B+sqrt%2810%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+=+2+%2B+3.1623+ ALIGN=MIDDLE  ALT=\"+x+=+2+%2B+3.1623+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+5.1623%0D%0ASo%2C+the+equation+is%3A%0D%0A%7B%7B%7B+y+=+-.5x%5E2+%2B+2x+%2B+3+ ALIGN=MIDDLE  ALT=\"+x+=+5.1623%0D%0ASo%2C+the+equation+is%3A%0D%0A%7B%7B%7B+y+=+-.5x%5E2+%2B+2x+%2B+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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+400%2C+400%2C+-2%2C+6%2C+-1%2C+6%2C+-.5x%5E2+%2B+2x+%2B+3+%29+ ALIGN=MIDDLE  ALT=\"+graph%28+400%2C+400%2C+-2%2C+6%2C+-1%2C+6%2C+-.5x%5E2+%2B+2x+%2B+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks close to answers<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );