Rewrite –4x3 +2y2 +3=0 so that all points on its graph are shifted 8 units up and 2 units to the left.

  -4(x +2)^3 +2(y -8)^2 +3 = 0

Step-by-step explanation:

To shift a function right by h units, replace x with x-h. Here, h = -2, so we want to substitute x+2 for x in the given equation.

To shift a function up by k units, replace y with y-k. Here, k = 8, so we want to substitute y-8 for y in the given equation.

Your translated graph has equation ...

  -4(x +2)^3 +2(y -8)^2 +3 = 0