The polynomial function f(x)=x^2-4x+1 has a critical point at which of the following x-values

A critical point exists when the derivative of the function equals 0 or does not exist.
First find the derivative.
f'(x) = 2x - 4

Set f'(x) = 0 to find cricial points.
0 = 2x - 4
x = 2

To find the y-value, substitute the x-value into the original f(x) equation.
f(x) = x^2 - 4x + 1
f(2) = (2)^2 - 4(2) + 1
= 4 - 8 + 1
= -3

The cricical point is (2, -3)