1. The problem states that the gradient (derivative) of the curve at any point $(x,y)$ is given by $2x - 4$. 2. We need to find the equation of the curve $y=f(x)$ such that its derivative $\frac{dy}{dx} = 2x - 4$. 3. To find $y$, integrate the derivative: $$y = \int (2x - 4) \, dx = \int 2x \, dx - \int 4 \, dx = x^2 - 4x + C$$ 4. Use the point $(3, 2)$ which lies on the curve to find $C$: $$2 = 3^2 - 4(3) + C$$ $$2 = 9 - 12 + C$$ $$2 = -3 + C$$ $$C = 5$$ 5. Therefore, the equation of the curve is: $$y = x^2 - 4x + 5$$ 6. Checking the options, this corresponds to option B. Final answer: $y = x^2 - 4x + 5$