Given the parent functions f (x) = x, the function g (x) = - (x + 7) 2 - 8 is

the result of shifts in the graph of Ax).

a. Describe the shift that takes fy) to g (x)

b. State the vertex of f (x)

c. State the axis of symmetry of g (x)

Step-by-step explanation:

Parent function f (x) = x²

a. Parent function f (x) when inverted about x - axis it becomes,

f' (x) = - x²

further f' (x) when shifted left by 7 units,

f" (x) = - (x + 7) ²

followed by a shift of 8 units downwards forms,

g (x) = - (x + 7) ² - 8

b. When we compare the function with vertex form of the quadratic function h (x) = - (x - h) ² + k

Vertex of the transformed function g (x) will be (-7, - 8)

c. Axis of symmetry of the function g (x) will be x = - 7.