To find the x-intercepts of the function \( y = x^2 - 9 \), we set \( y = 0 \):
\[ 0 = x^2 - 9 \ x^2 = 9 \ x = 3 \quad \text{or} \quad x = -3 \]
So, the x-intercepts are at \( (3, 0) \) and \( (-3, 0) \).
Now, when the graph is reflected over the x-axis, we change the function to \( y = - (x^2 - 9) = -x^2 + 9 \).
The new equation is \( y = -x^2 + 9 \). To find the new x-intercepts, we again set \( y = 0 \):
\[ 0 = -x^2 + 9 \ x^2 = 9 \ x = 3 \quad \text{or} \quad x = -3 \]
Thus, reflecting the graph over the x-axis does not change the x-intercepts; they remain at \( (3, 0) \) and \( (-3, 0) \).
Therefore, the correct response is:
The x-intercepts stay the same.
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