What would be the parent function related to the function y = 3 (x + 2) 4?

Answer: y = x^4

This is the standard basic quartic equation which graphs something that looks very similar to a parabola (but it's not actually a parabola). This has degree 4.

To go from y = x^4 to y = 3 (x+2) ^4, we shift 2 units to the left getting y = (x+2) ^4, then we vertically stretch by a factor of 3 to get y = 3 (x+2) ^4