Question

Which function has an axis of symmetry of x = −2?

f(x) = (x − 1)^2 + 2
f(x) = (x + 1)^2 − 2
f(x) = (x − 2)^2 − 1
f(x) = (x + 2)^2 − 1

Answer 1

D. f(x) = (x + 2)2 − 1

Explanation:

Answer 2

All of these functions start from the same function, f(x) = x^2, which has an axis of symmetry of x = 0, but they have all been shifted horizontally and vertically.
The first function has been shifted 1 unit to the right and 2 units up, having an axis of symmetry at x = 1.
The second function has been shifted 1 unit to the left and 2 units down, having an axis of symmetry at x = -1.
The third function has been shifted 2 units to the right and 1 unit down, having an axis of symmetry at x = 2.
The fourth function has been shifted 2 units to the left and 1 unit down, having an axis of symmetry at x = -2.
As you can see, because the last function has been shifted 2 units to the left, its axis of symmetry is at x = -2.

Final Answer:
The fourth function, f(x) = (x+2)^2-1 has an axis of symmetry of x = -2.
Hope I helped :)