To determine the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to write the new function.
The new function after translating \( f(x) \) down 4 units is:
\[ g(x) = f(x) - 4 = x^2 - 4 \]
Next, we find the x-intercepts by setting \( g(x) = 0 \):
\[ x^2 - 4 = 0 \]
Now, we can solve this equation:
\[ x^2 = 4 \]
Taking the square root of both sides gives us:
\[ x = \pm 2 \]
Thus, the x-intercepts are:
\[ x = 2 \quad \text{and} \quad x = -2 \]
So the correct response is:
x equals negative 2 and x equals 2.