The equation of y = x³ with given transformations can be written as y = -3(x + 2)³ - 2.
The equation of y = x³ with the given transformations is as follows:
Vertical stretch by a factor of 3: Multiply the equation by 3, which will result in y = 3x³.
Reflection in the x-axis: Negate the y-value of the equation, giving you y = -3x³.
Vertical translation 2 units down: Subtract 2 from the equation, giving you y = -3x³ - 2.
Horizontal translation 2 units left: Replace every x in the equation with (x + 2), resulting in y = -3(x + 2)³ - 2.
So, the equation with the given transformations is y = -3(x + 2)³ - 2.