What happens to the x-intercepts of the function y=x2−25

Question

when the graph is reflected over the x-axis? Explain.(1 point)
Responses

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.
The x -values and y -values switch.

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

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

Answer 1

The correct response is:

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

Here's the explanation:

When reflecting a function over the x-axis, the y-values of all points on the graph are negated. However, the x-intercepts are the points where the function crosses the x-axis, which occur when \( y = 0 \). Since \( 0 \) remains the same even when negated (i.e., \( -0 = 0 \)), the x-intercepts do not change. Therefore, they remain at the same x-coordinates regardless of reflection. The function \( y = x^2 - 25 \) has x-intercepts at \( x = 5 \) and \( x = -5 \), and these will still be the same after reflecting the graph over the x-axis.