Check the picture below, that's a transformation's template.
now, can f(x) = 2(x+3)² obtained from f(x) = x² by simply translating the parent x²?
well, let's notice, there's a horizontal shift or translation to the left with the +3 or namely C = +3 whilst B = 1, so the shift is 3/1 or just 3 to the left, that's true, however A = 2, that'll make it shrink by half, making 2(x+3)² a narrower parabola than its parent x².