To find the real zeros of the function y = 2(x - 3)^3 + 4, set the function equal to zero and solve for x:
2(x - 3)^3 + 4 = 0
Subtract 4 from both sides:
2(x - 3)^3 = -4
Divide by 2:
(x - 3)^3 = -2
Now, take the cube root of both sides:
x - 3 = ∛(-2)
x - 3 ≈ -1.26 (approximate cube root of -2)
Now, solve for x:
x ≈ -1.26 + 3
x ≈ 1.74
So, the real zero of the function is approximately x = 1.74.