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 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.

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-values and y-values switch.

Answer 1

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 where \( y = 0 \):

\[ 0 = x^2 - 25 \]

Solving for \( x \):

\[ x^2 = 25 \] \[ x = 5 \quad \text{or} \quad x = -5 \]

So the x-intercepts are at \( (5, 0) \) and \( (-5, 0) \).

When the graph is reflected over the x-axis, the y-values are negated. However, since the y-values for the x-intercepts are both \( 0 \) (the points are on the x-axis), negating \( 0 \) still gives \( 0 \). Therefore, the x-intercepts themselves do not change in their positions.

Thus, the correct response is:

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