For a quadratic function ax² + bx + c where a > 0, the minimum occurs at x = -b/2a. Here, x = -(-4)/(2*1) = 2. Substituting x=2 into the function: f(2) = (2)² - 4(2) + 7 = 4 - 8 + 7 = 3. Alternatively, completing the square gives f(x) = (x-2)² + 3, where the minimum value is clearly 3 when the squared term is zero.