Question

What happens to the x-intercepts of the function y=x2−9
when the graph is reflected over the x-axis?(1 point)
Responses

The x-intercepts get shifted down 9 units.
The x-intercepts get shifted down 9 units.

The x-intercepts stay the same.
The x-intercepts stay the same.

There are no x-intercepts.
There are no x-intercepts.

The x-intercepts get shifted to the right 9 units.

Answer 1

To determine what happens to the x-intercepts of the function \( y = x^2 - 9 \) when the graph is reflected over the x-axis, we need to first find the x-intercepts of the original function.

The x-intercepts occur where \( y = 0 \):
\[
0 = x^2 - 9
\]
This simplifies to:
\[
x^2 = 9
\]
Taking the square root of both sides gives us:
\[
x = 3 \quad \text{and} \quad x = -3
\]
So the x-intercepts of the function \( y = x^2 - 9 \) are at the points \( (3, 0) \) and \( (-3, 0) \).

Now, when we reflect the entire graph over the x-axis, every point \((x, y)\) on the graph becomes \((x, -y)\). As a result, the points where the original function had x-intercepts will now correspond to:
\[
(3, 0) \text{ and } (-3, 0)
\]
After reflection, the y-coordinates of the x-intercepts remain the same (they still have a y-value of 0). Therefore, the x-intercepts themselves do not change in terms of their x-values.

The correct response is:

**The x-intercepts stay the same.**