To reflect the function \( f(x) = (x + 1)^2 \) about the origin, we need to transform both \( x \) and \( y \) coordinates. This is done by replacing \( f(x) \) with \( -f(-x) \).
First, let's calculate \( f(-x) \): \[ f(-x) = (-x + 1)^2 = (1 - x)^2 \]
Now we can find \( -f(-x) \): \[ -f(-x) = - (1 - x)^2 \]
Next, we reflect the point \( (-4, 9) \). The x-coordinate after reflection will be \( x' = -(-4) = 4 \). The original y-coordinate \( y = 9 \) will become \( y' = -9 \).
Now, we compute the new point: So, the reflected point is \( (4, -9) \).
In conclusion, the point \( (-4, 9) \) reflects to \( (4, -9) \) in the function \( -f(-x) \).