document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177358>Question 1177358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3.    The function h = −0.25 d² + 0.8d models the height, h meters, of a soccer ball in terms of the horizontal distance, d meters, from where the ball was kicked. <BR>\n" );
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document.write( "a)    Find the horizontal distance the ball travels until it first hits the ground. Show work.<BR>\n" );
document.write( "Use both the factoring method and the quadratic formula method to obtain your answer. <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 #806322 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=806322\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Find the horizontal distance the ball travels until it first hits the ground. Show work.<BR>\n" );
document.write( "Use both the factoring method and the quadratic formula method to obtain your answer.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.25d%5E2+%2B+0.8d ALIGN=MIDDLE  ALT=\"h=+-0.25d%5E2+%2B+0.8d\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "when a soccer ball hits the ground,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h=0+ ALIGN=MIDDLE  ALT=\"+h=0+\"   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=0=+-0.25d%5E2+%2B+0.8d ALIGN=MIDDLE  ALT=\"0=+-0.25d%5E2+%2B+0.8d\"   DISABLED_style= \"max-width:90%; height:auto;\" >......factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=+%28-0.25d+%2B+0.8%29d ALIGN=MIDDLE  ALT=\"0=+%28-0.25d+%2B+0.8%29d\"   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=d=0 ALIGN=MIDDLE  ALT=\"d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-0.25d+%2B+0.8=0+ ALIGN=MIDDLE  ALT=\"-0.25d+%2B+0.8=0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.8=0.25d+ ALIGN=MIDDLE  ALT=\"0.8=0.25d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d=0.8%2F0.25 ALIGN=MIDDLE  ALT=\"+d=0.8%2F0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3.2 ALIGN=MIDDLE  ALT=\"d=3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using the quadratic formula method:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.25d%5E2+%2B+0.8d ALIGN=MIDDLE  ALT=\"h=+-0.25d%5E2+%2B+0.8d\"   DISABLED_style= \"max-width:90%; height:auto;\" >  => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-0.25 ALIGN=MIDDLE  ALT=\"a=-0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b=+0.8 ALIGN=MIDDLE  ALT=\"+b=+0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=0 ALIGN=MIDDLE  ALT=\"c=0\"   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=d=%28-0.8%2B-sqrt%280.8%5E2-4%28-0.25%29%2A0%29%29%29%2F%282%28-0.25%29%29 ALIGN=MIDDLE  ALT=\"d=%28-0.8%2B-sqrt%280.8%5E2-4%28-0.25%29%2A0%29%29%29%2F%282%28-0.25%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=d=%28-0.8%2B-sqrt%280.8%5E2%29%29%2F%28-0.50%29 ALIGN=MIDDLE  ALT=\"d=%28-0.8%2B-sqrt%280.8%5E2%29%29%2F%28-0.50%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=d=%28-0.8%2B-0.8%29%2F%28-0.50%29 ALIGN=MIDDLE  ALT=\"d=%28-0.8%2B-0.8%29%2F%28-0.50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28-0.8%2B0.8%29%2F%28-0.50%29=0%2F-0.50=0 ALIGN=MIDDLE  ALT=\"d=%28-0.8%2B0.8%29%2F%28-0.50%29=0%2F-0.50=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%28-0.8-0.8%29%2F%28-0.50%29=-1.6%2F-0.50=3.2 ALIGN=MIDDLE  ALT=\"d=%28-0.8-0.8%29%2F%28-0.50%29=-1.6%2F-0.50=3.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the horizontal distance the ball travels until it first hits the ground\r<BR>\n" );
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document.write( "in case you need these questions:\r<BR>\n" );
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document.write( "b) Find the horizontal distance when the ball reaches its maximum height. Make a sketch. Show work.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.25d%5E2+%2B+0.8d ALIGN=MIDDLE  ALT=\"h=+-0.25d%5E2+%2B+0.8d\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "max is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertex ALIGN=MIDDLE  ALT=\"vertex\"   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=-b%2F2a=-0.8%2F%282%28-0.25%29%29=1.6 ALIGN=MIDDLE  ALT=\"-b%2F2a=-0.8%2F%282%28-0.25%29%29=1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the horizontal distance when the ball reaches its maximum height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=1.6 ALIGN=MIDDLE  ALT=\"d=1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c) Find the maximum height of the ball using the distance you just determined in part b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+ ALIGN=MIDDLE  ALT=\"h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+ ALIGN=MIDDLE  ALT=\"h=+-0.25%2A1.6%5E2+%2B+0.8%2A1.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.64%2B+1.28+ ALIGN=MIDDLE  ALT=\"h=+-0.64%2B+1.28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+0.64+ ALIGN=MIDDLE  ALT=\"h=+0.64+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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