The given expression is a convex quadratic, so the extremum is a minimum. It is known that if f is a quadratic and f(a)=f(b), then the extremum value of f(x) is achieved on x=a+b2. Let f be the given expression.
Note that f(0)=f(−20), thus the minimum of f is f(−10)=∑20k=−20k24=1435.