Final answer:
The transformed function is f(x) = -(x + 8)^2 + 9 .
Step-by-step explanation:
To transform the function f(x) = x^2 according to the given instructions (moved eight units to the left, nine units upward, and then reflected in the x-axis), we perform the following steps:
1. Move eight units to the left:
This transformation is represented as f(x + 8) , meaning that for any value of x in the original function, we replace it with x + 8. This shifts the graph horizontally to the left.
2. Move nine units upward:
Adding 9 to the function shifts the entire graph vertically upward. The transformation is represented as f(x + 8) + 9.
3. Reflect in the x-axis:
The reflection in the x-axis is represented by the negative sign outside the function. This reflects the graph vertically.
Putting it all together, the transformed function is f(x) = -(x + 8)^2 + 9. This means that the original function f(x) = x^2 has been shifted eight units to the left, nine units upward, and then reflected in the x-axis.