document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=683994>Question 683994</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A programmer is writing the code for a new interactive basketball game. As a result, she is using quadratic relations to model the path of the ball. During the game, when a ball is shot, the path it follows is modeled by the quadratic relation,h= -0.2d^2 + 3d + 6 , where h represented the height of the ball above the ground and d represented the distance of the ball from the shooter. Both distances are measured in feet.\r<BR>\n" );
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document.write( "How high was the ball when the shooter shot it?<BR>\n" );
document.write( "What was the maximum height obtained by the ball?<BR>\n" );
document.write( "A rim of a basketball net is 10 feet high. For what horizontal distance was the ball above the rim of the basketball net?\r<BR>\n" );
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document.write( "Please help for my review coming up ): </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #423860 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=423860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How high was the ball when the shooter shot it?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.2d%5E2+%2B+3d+%2B+6 ALIGN=MIDDLE  ALT=\"h=+-0.2d%5E2+%2B+3d+%2B+6\"   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=h=+-0.2%280%29%5E2+%2B+3%280%29+%2B+6 ALIGN=MIDDLE  ALT=\"h=+-0.2%280%29%5E2+%2B+3%280%29+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > ... Plug in d = 0 (since the ball is zero ft away from the player when it is shot)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=+-0.2%280%29+%2B+3%280%29+%2B+6+ ALIGN=MIDDLE  ALT=\"h=+-0.2%280%29+%2B+3%280%29+%2B+6+\"   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=h=+0+%2B+0+%2B+6+ ALIGN=MIDDLE  ALT=\"h=+0+%2B+0+%2B+6+\"   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=h+=+6 ALIGN=MIDDLE  ALT=\"h+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the ball is 6 ft off the ground when the shooter shot it.\r<BR>\n" );
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document.write( "What was the maximum height obtained by the ball?\r<BR>\n" );
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document.write( "To answer this question, we need to find the vertex\r<BR>\n" );
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document.write( "First replace all 'h' terms with y. Then replace all 'd' terms with 'x'\r<BR>\n" );
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document.write( "Now find the x coordinate of the vertex\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-3%2F%282%28-0.2%29%29 ALIGN=MIDDLE  ALT=\"x+=+-3%2F%282%28-0.2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then plug this in to find the y coordinate of the vertex\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-0.2%287.5%29%5E2+%2B+3%287.5%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+-0.2%287.5%29%5E2+%2B+3%287.5%29+%2B+6\"   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=y+=+-0.2%2856.25%29+%2B+3%287.5%29+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+-0.2%2856.25%29+%2B+3%287.5%29+%2B+6\"   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=y+=+-11.25+%2B+22.5+%2B+6 ALIGN=MIDDLE  ALT=\"y+=+-11.25+%2B+22.5+%2B+6\"   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=y+=+17.25 ALIGN=MIDDLE  ALT=\"y+=+17.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The y coordinate of the vertex represents the highest point.\r<BR>\n" );
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document.write( "So the max height is 17.25 ft.\r<BR>\n" );
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document.write( "A rim of a basketball net is 10 feet high. For what horizontal distance was the ball above the rim of the basketball net? \r<BR>\n" );
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document.write( "Plug in h = 10 and solve for d\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+-0.2d%5E2+%2B+3d+%2B+6 ALIGN=MIDDLE  ALT=\"10+=+-0.2d%5E2+%2B+3d+%2B+6\"   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%5E2+-+15d+%2B+20+=+0%2F2 ALIGN=MIDDLE  ALT=\"d%5E2+-+15d+%2B+20+=+0%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the quadratic formula to solve for d\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%28-%28-15%29%2B-sqrt%28%28-15%29%5E2-4%281%29%2820%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"d+=+%28-%28-15%29%2B-sqrt%28%28-15%29%5E2-4%281%29%2820%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+1 ALIGN=MIDDLE  ALT=\"a+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-15 ALIGN=MIDDLE  ALT=\"b+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+20 ALIGN=MIDDLE  ALT=\"c+=+20\"   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+=+%2815%2B-sqrt%28225-%2880%29%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"d+=+%2815%2B-sqrt%28225-%2880%29%29%29%2F%282%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+=+%2815%2B-sqrt%28145%29%29%2F2 ALIGN=MIDDLE  ALT=\"d+=+%2815%2B-sqrt%28145%29%29%2F2\"   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+=+%2815%2Bsqrt%28145%29%29%2F2 ALIGN=MIDDLE  ALT=\"d+=+%2815%2Bsqrt%28145%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+%2815-sqrt%28145%29%29%2F2 ALIGN=MIDDLE  ALT=\"d+=+%2815-sqrt%28145%29%29%2F2\"   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+=+13.520797 ALIGN=MIDDLE  ALT=\"d+=+13.520797\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+1.479203 ALIGN=MIDDLE  ALT=\"d+=+1.479203\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the distance is either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+13.520797 ALIGN=MIDDLE  ALT=\"d+=+13.520797\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+1.479203 ALIGN=MIDDLE  ALT=\"d+=+1.479203\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which means that the distance it travels about 13.520797 - 1.479203 = 12.041594 feet horizontally when the ball is above the 10 ft rim. </SPAN>\n" );
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