To reflect the function \( f(x) = (x + 1)^2 \) about the origin, we first need to transform the function accordingly. Reflecting around the origin means we take \( f(-x) \) and multiply it by -1.
-
Calculate \( f(-x) \): \[ f(-x) = (-x + 1)^2 = (1 - x)^2 \]
-
Now negate this function: \[ -f(-x) = - (1 - x)^2 \]
-
Now let's determine the coordinates of the reflection of the point (-4, 9):
- The original point is \((-4, 9)\).
- The reflection across the origin involves taking both coordinates and negating them.
Hence, reflecting the point: \[ (-4, 9) \rightarrow (4, -9) \]
So the reflected position of the point (-4, 9) in the reflected function \( -f(-x) \) is \((4, -9)\).
Therefore, the answer is: \[ (4, -9) \]