To analyze what happens to the x-intercepts of the function \( y = x^2 - 25 \) when the graph is reflected over the x-axis, we first need to determine the x-intercepts of the function.
The x-intercepts of a function are found where \( y = 0 \). So we set up the equation:
\[ 0 = x^2 - 25 \]
Solving this, we get:
\[ x^2 = 25 \] \[ x = 5 \quad \text{or} \quad x = -5 \]
Thus, the x-intercepts of the function are at the points \( (5, 0) \) and \( (-5, 0) \).
When we reflect the graph over the x-axis, the y-values of all points are negated. So, the points \( (5, 0) \) and \( (-5, 0) \) become \( (5, 0) \) and \( (-5, 0) \) again because their y-values are still 0.
This shows that the x-intercepts remain unchanged after the reflection over the x-axis since the x-intercepts are defined by the points where the function equals zero (where y is zero).
So, the correct response is:
The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.