Find the range of a $4$th-degree function For the function $y=(x-1)(x-2)(x-3)(x-4)$, I see graphically that the range is $\ge-1$.  But I cannot find a way to determine the range algebraically?

Non-calculus Approach/ Completing Square Approach
Let $u=(x-2)(x-3)=x^2-5x+6$
$(x-1)(x-4)=x^2-5x+4=u-2$
So 
\begin{align}
y&=(x-1)(x-2)(x-3)(x-4)\\&=u(u-2)\\&=u^2-2u\\&=(u-1)^2-1
\end{align}
As $(u-1)^2\ge0$ for all $u\in{\Bbb{R}}$
$y\ge0-1=-1$
