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 occur when \( y = 0 \). Setting the equation to zero gives us:
\[ 0 = x^2 - 25 \]
Solving for \( x \) gives:
\[ x^2 = 25 \] \[ x = \pm 5 \]
So, the x-intercepts of the function are \( x = 5 \) and \( x = -5 \).
When the graph is reflected over the x-axis, the y-values of the function change signs. Specifically, if we reflect the function \( y = x^2 - 25 \) over the x-axis, we get the new function:
\[ y = -(x^2 - 25) = -x^2 + 25 \]
Now we can observe that the x-intercepts do not depend on the y-values, but rather on where the function intersects the x-axis. The x-intercepts remain at \( x = 5 \) and \( x = -5 \) because the values of \( x \) that make \( y = 0 \) are unchanged.
Therefore, the correct response is:
The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.