Without calculus...
y=5x^2-20x+1357
y-1357=5x^2-20x
(y-1357)/5=x^2-4x
(y-1357)/5+4=x^2-4x+4
(y-1357)/5+4=(x-2)^2
(y-1357)/5=(x-2)^2-4
y-1357=5(x-2)^2-20
y=5(x-2)^2+1337
So the minimum value for y is 1337
With calculus...
y=5x^2-20x+1357
dy/dx=10x-20
dy/dx=0 when
10x-20=0
10x=20
x=2
y(2)=5(4)-20(2)+1357=1337