What are all the real zeros of y=(x-12)^3 -10?
Suppose you had
x^3-10 = 0
Then the only real zero would be x=∛10, right?
Well, this is the same thing. The only real zero is
x-12 = ∛10, or
x = 12+∛10
The graph is just like the graph of x^3-10, but shifted right by 12.
To find the real zeros of the function y = (x-12)^3 - 10, we need to solve for x when y equals zero.
Setting y = 0, we have:
0 = (x-12)^3 - 10
First, let's add 10 to both sides to get rid of the constant term:
10 = (x-12)^3
Now, we can take the cube root of both sides to isolate x - 12:
∛10 = x - 12
To find the real zeros, we'll simplify ∛10 and add 12 to both sides:
x = ∛10 + 12
So, the real zero of y = (x-12)^3 - 10 is x = ∛10 + 12.