1. The problem is to find the roots of the function $y(x) = 2(x-1)^2$. 2. Roots of a function are the values of $x$ for which $y(x) = 0$. 3. Set the function equal to zero: $$2(x-1)^2 = 0$$ 4. Divide both sides by 2: $$\cancel{2}(x-1)^2 = \cancel{2}0$$ $$ (x-1)^2 = 0$$ 5. Take the square root of both sides: $$x-1 = 0$$ 6. Solve for $x$: $$x = 1$$ 7. Therefore, the root of the function is $x = 1$. This means the graph touches the x-axis at $x=1$ and does not cross it because the root has multiplicity 2.