document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254211>Question 254211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The vertical height, h, in metres of a golf ball as it travels a horizontal distance, d metres, down the fairway, can be described using a quadratic function.  A pro-golfer can drive the ball 300m down the fairway before it lands.  If the ball's maximum height was 15m:\r<BR>\n" );
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document.write( "- draw a sketch of the path of the golf ball<BR>\n" );
document.write( "- find the equation of the path of the golf ball<BR>\n" );
document.write( "- determine the two distances down the fairway when the ball is 10m above the ground.  Give your answer to the nearest tenth of a metre. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186691 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "We are looking for a function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(d)\">\r<BR>\n" );
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document.write( "such that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(0)\ =\ 0\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(300)\ =\ 0\">\r<BR>\n" );
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document.write( "We are given that this is a quadratic function, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(d)\ =\ ad^2\ +\ bd\ +\ c\">\r<BR>\n" );
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document.write( "The graph is a parabola with the vertex on the axis of symmetry, namely half-way between <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ 0\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ 300\">, to wit:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large d\ =\ 150\">  and we are given that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(150)\ =\ 15\">\r<BR>\n" );
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document.write( "So from\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(0)\ =\ 0\">\r<BR>\n" );
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document.write( "we can deduce that <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large c\ =\ 0\"> in\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(d)\ =\ ad^2\ +\ bd\ +\ c\">\r<BR>\n" );
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document.write( "and then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(d)\ =\ ad^2\ +\ bd\">\r<BR>\n" );
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document.write( "remains.  Then, from\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(300)\ =\ 0\">\r<BR>\n" );
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document.write( "we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(300)\ =\ 90000a\ +\ 300b\ =\ 0\">\r<BR>\n" );
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document.write( "and from\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(150)\ =\ 15\">\r<BR>\n" );
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document.write( "we can write:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ h(150)\ =\ 22500a\ +\ 150b\ =\ 15\">\r<BR>\n" );
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document.write( "Giving us a system of two linear equations in two variables.  I recommend that you solve them by the elimination method.  Once you have the coefficients for the quadratic, set the quadratic expression equal to 10 and solve for the two roots.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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