Question

The parent function f(x) = x2 is translated such that the function g(x) = –x2 + 6x – 5 represents the new function. What is true about the transformation that was performed? Check all that apply.
g(x) has an axis of symmetry at x = 3.
g(x) is shifted down 5 units from the graph of f(x).
g(x) is shifted right 3 units from the graph of f(x).
g(x) is shifted up 4 units from the graph of f(x).
g(x) is narrower than f(x).

Answer 1

G(x)=-(x^2-6x+5)
      =-(x-6x+9-9+5)
      =-(x-3)²+4
It is reflected across the a axis, shifted 3 units to the right, shifted 4 units up, and It has an axis of symmetry at x=3

Answer 2

A -g(x) has an axis of symmetry at x = 3. 
C -g(x) is shifted right 3 units from the graph of f(x).
D -g(x) is shifted up 4 units from the graph of f(x).