Question

If the function f(x) = (x +3)^2 is reflected over the x-axis then how does the reflection affect the point (2,25)

Answer 1

To find how the reflection of the function \( f(x) = (x + 3)^2 \) over the x-axis affects the point \( (2, 25) \), we begin by determining the reflection of the function itself.

1. **Reflection Over the x-axis**: To reflect the function over the x-axis, we change the sign of the function. Therefore, the reflected function is:

\[
g(x) = -f(x) = -(x + 3)^2
\]

2. **Evaluating the Reflected Function at the x-coordinate**: Now we will find the new y-coordinate for the point where \( x = 2 \):

\[
g(2) = -(2 + 3)^2 = -(5)^2 = -25
\]

3. **Determining the Reflected Point**: The original point is \( (2, 25) \), meaning the x-coordinate is 2 and the y-coordinate is 25. After reflecting over the x-axis, the new y-coordinate becomes \(-25\), while the x-coordinate remains the same.

Thus, the reflected point is:

\[
(2, -25)
\]

In summary, when the function \( f(x) = (x + 3)^2 \) is reflected over the x-axis, the point \( (2, 25) \) becomes \( (2, -25) \).