What is the equation of the graph obtained when the parent graph y=x^3 translated 4 units left and 7 units down?

y = (x + 4)³ - 7

Step-by-step explanation:

Parent function describes the general formula of a graph without a translation, or shift of any kind.  When considering how these shifts affect the graph, a translation to the left or right would affect the x-axis and a translation up or down would affect the y-axis.  When the x-axis is affected, that constant must be connected to the variable 'x', while a movement up or down must be separated and connected to the variable 'y'.  In the case of the parent function y = x³, adding '4' to the variable 'x' would shift the graph left and subtracting the '7' as a constant of the expression would move the graph down:

y = (x + 4)³ - 7

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