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.
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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:
\[ g(x) = -f(x) = -(x + 3)^2 \]
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Evaluating the Reflected Function at the x-coordinate: Now we will find the new y-coordinate for the point where \( x = 2 \):
\[ g(2) = -(2 + 3)^2 = -(5)^2 = -25 \]
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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 \( (2, -25) \).