To determine the effect of reflecting the function \( y = x^2 - 25 \) over the x-axis, we need to analyze the concept of x-intercepts. The x-intercepts are found by setting \( y = 0 \):
\[ 0 = x^2 - 25 \] Solving for \( x \) gives:
\[ x^2 = 25 \ x = 5 \quad \text{or} \quad x = -5 \]
Thus, the x-intercepts of the function are at \( x = 5 \) and \( x = -5 \).
When we reflect the graph of a function over the x-axis, the new function becomes \( y = -f(x) \). For our function, this results in:
\[ y = -(x^2 - 25) = -x^2 + 25 \]
The x-intercepts of the new function are found by setting \( y = 0 \):
\[ 0 = -x^2 + 25 \ x^2 = 25 \ x = 5 \quad \text{or} \quad x = -5 \]
Thus, the x-intercepts remain the same at \( x = 5 \) and \( x = -5 \) after the reflection.
Therefore, the correct response is:
The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.