The equation after the sequence of transformations is
g(x) = - (x - 9)².+ 16
Description of the transformation
The parent function is f(x) = x².
Translation right 9 units:
This transformation is represented by (x - 9)².
Translation up 16 units
This is represented by (x - 9)².+ 16
Reflection across the x-axis:
This is represented by -(x - 9)².+ 16
Combining these transformations, the function g(x) is given by:
g(x) = - (x - 9)².+ 16