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 reflect the function \( f(x) = (x + 3)^2 \) over the x-axis, we take the negative of the function. The reflected function is given by:

\[ f_{\text{reflected}}(x) = -f(x) = -(x + 3)^2 \]

Now, let's consider the effect of this reflection on the specific point \( (2, 25) \).

1. First, we check if the point \( (2, 25) \) lies on the original function: \[ f(2) = (2 + 3)^2 = 5^2 = 25 \] Thus, the point \( (2, 25) \) is indeed on the original function \( f(x) \).

2. Next, we reflect this point over the x-axis. The reflection of a point \( (x, y) \) over the x-axis is given by the point \( (x, -y) \). Therefore, the reflection of the point \( (2, 25) \) is: \[ (2, -25) \]

So, after reflecting the point \( (2, 25) \) over the x-axis, we obtain the new point \( (2, -25) \).