Question

If the function f of x equals (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 change the function to \( f(x) = -(x + 3)^2 \). This reflection means that for any point \( (x, y) \) on the original function, the corresponding point on the reflected function will be \( (x, -y) \).

The point given is \( (2, 25) \). We need to determine if this point is on the original function \( f(x) \).

Calculating \( f(2) \):
\[
f(2) = (2 + 3)^2 = 5^2 = 25
\]
So, the point \( (2, 25) \) is indeed on the function \( f(x) \).

To find the corresponding point after reflection over the x-axis, we change the y-coordinate:
\[
(2, 25) \rightarrow (2, -25)
\]

Thus, the reflection of the point \( (2, 25) \) over the x-axis is \( (2, -25) \).