Question

What happens to the x-intercepts of the function y=x2−25
when the graph is reflected over the x-axis? Explain.(1 point)
Responses

This function does not have any x-intercepts, so no changes are necessary.
This function does not have any x -intercepts, so no changes are necessary.

The x-intercepts become negated.
The x -intercepts become negated.

The x-intercepts remain the same because the y-values get negated during a reflection over the x-axis.
The x -intercepts remain the same because the y -values get negated during a reflection over the x -axis.

The x-values and y-values switch.

Answer 1

The x-intercepts remain the same: y = x^2 − 25 has x-intercepts at x = ±5. Reflecting over the x-axis gives y' = −(x^2 − 25) = −x^2 + 25, and solving y' = 0 still yields x^2 = 25, x = ±5. Zeros stay zeros because negating y does not change where y = 0.