Sketchorama
Sketch the graph of the curve $y^2 = x(2−x)$
Age
14 to 16
Challenge level
Problem
Sketch the graph of the curve $y^{2} = x(2 - x)$
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
We have $y^{2}=x(2-x)$.
$y^{2}\ge0$ for all real $y$, hence $x(2-x)\ge0$.
Hence $0\le x\le2$.
In fact we can rewrite the equation as $(x-1)^{2}+y^{2}=1$
So this is a circle of radius $1$ with centre at $(1,0)$.