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

Question

Responses

The x-values and y-values switch.
The x -values and y -values switch.

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 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-intercepts become negated.

Answer 1

To understand 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 identify the x-intercepts of the original function.

The x-intercepts occur where $y=0$:

$$0=x^2-25$$ $$x^2=25$$ $$x=5\text{or}x=-5$$

So, the x-intercepts of the function $y=x^2-25$ are at $x=5$ and $x=-5$.

When the graph is reflected over the x-axis, the new function would be $y=-(x^2-25)=-x^2+25$.

In this new function, the x-intercepts are found by setting $y=0$ again:

$$0=-x^2+25$$ $$x^2=25$$ $$x=5\text{or}x=-5$$

Thus, the x-intercepts remain at $x=5$ and $x=-5$.

The correct response to the question is:

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