Question

if the function $f(x) = (x + 3)^2$ is reflected over the x - axis, then how does the reflection affect the point $(2, 25)$? (1 point)
in the reflection, the point $(2, 25)$ becomes $(-2, 25)$.
in the reflection, the point $(2, 25)$ becomes $(2, -25)$.
in the reflection, the point $(2, 25)$ becomes $(-2, -25)$.
in the reflection, the point $(2, 25)$ becomes $(2, -125)$.

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, if we have a point \((x,y)\), after reflection over the \(x\) - axis, the new point is \((x, - y)\).

Step2: Identify the original point

We are given the point \((2,25)\). Here, \(x = 2\) and \(y=25\).

Step3: Apply the reflection rule

Using the rule for reflection over the \(x\) - axis, when we reflect the point \((2,25)\) over the \(x\) - axis, the \(x\) - coordinate (which is \(2\)) stays the same, and the \(y\) - coordinate (which is \(25\)) becomes \(- 25\). So the new point is \((2,-25)\).

Answer:

In the reflection, the point \((2,25)\) becomes \((2, - 25)\) (the option corresponding to this description).