9436 /www/nrich/html/content/id/9436/ 1 2012-09-18T13:17:53 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br> Sketch the graph of the curve $y^{2} = x(2 - x)$<br></br> <br></br> <br></br> <br></br> <br></br> If you liked this problem, <a href="/5872">here is an NRICH task</a> which challenges you to use similar mathematical ideas.<br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br> <br></br> We have $y^{2}=x(2-x)$.<br></br> <br></br> $y^{2}\ge0$ for all real $y$, hence $x(2-x)\ge0$.<br></br> <br></br> Hence $0\le x\le2$.<br></br> <br></br> In fact we can rewrite the equation as $(x-1)^{2}+y^{2}=1$<br></br> <br></br> So this is a circle of radius $1$ with centre at $(1,0)$.<br></br> <br></br> <br></br> <br></br> <br></br> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Graphs of Functions - Stage 4 Short Problem, UKMT 2009-2010 p112 Q18</mdoxml> 2 3 0 0 0 1 0 Sketch the graph of the curve $y^2 = x(2−x)$ Secondary Mapping Document DisplayCabinet Secondary Mapping Document Graphs of functions