At the point where the tangent is parallel to the x- axis, the slope of the curve = 0. Given: \(y = x^{2} - 4x + 3\) \(\frac{\mathrm d y}{\mathrm d x} = 2x - 4\) \(2x - 4 = 0 \implies 2x = 4 \) \(x = 2\) When x = 2, the tangent of the curve is parallel to the x- axis.