Question

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)

Answer 1

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.