Factorise f(x) = x^2+4x+4 and sketch the curve, identifying the roots and minimum point of f(x).

f(x) = (x+2)(x+2) When f(x) = 0, x = -2. f'(x) = 2x + 4 When f'(x) = 0, x = -2, and corresponds to the minimum point. Therefore, the sketch of the curve will be a U-shaped parabola which touches the x-axis at x = -2 and crosses the y-axis at y = 4.