To find the x-intercepts of the function \( f(x) = x^2 \) translated down 4 units, we start by rewriting the function:
\[ f(x) = x^2 - 4 \]
Next, to determine the x-intercepts, we set the function equal to zero:
\[ x^2 - 4 = 0 \]
We can factor the equation:
\[ (x - 2)(x + 2) = 0 \]
Setting each factor equal to zero gives us the potential x-intercepts:
\[ x - 2 = 0 \quad \Rightarrow \quad x = 2 \] \[ x + 2 = 0 \quad \Rightarrow \quad x = -2 \]
Thus, the x-intercepts of the translated function are:
\[ x = -2 \quad \text{and} \quad x = 2 \]
So the correct response is:
x=−2 and x=2.