If f(x) =x^2 - 5x + 7 what are the coordinates of the minimum of f(x-2)?

The easiest way to do this is to notice that f(x-2) is just f(x) translated by two in the positive x-direction - it is not necessary to calculate what f(x-2) is at any point!
So we calculate f'(x) = 2x - 5Set f'(x) = 0 = 2x-5 to find that x = 2.5
So the corresponding value that minimises f(x-2) will be 4.5 as f(x-2) has been translated by two in the positive x-direction.
The value of y at this point will be 2.5^2 - 5 * 2.5 + 7 = 6.25 - 12.5 + 7 = 0.75
So our final answer is (4.5, 0.75) or (9/2, 3/4) in fraction form.