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

(x + 2)^2 - 1

Explanation:

The parent function of a quadratic function is y = x^2 with an axis of symmetry at x = 0. All of the given possible answer choices show transformations being applied to the parent function. Transforming the function left or right also changes the axis of symmetry. Thus, we need to find the transformed function that shifts the parent function two times to the left (this means a positive two is applied inside the parentheses to x):

(x - 1)^2 + 2 shifts the function right 1 and up 2, thus the axis of symmetry is x = 1

(x + 1)^2 - 2 shifts the function left 1 and down 2, thus the axis of symmetry is x = -1

(x - 2)^2 - 1 shifts the function right 2 and down 1, thus the axis of symmetry is x = 2

(x + 2)^2 - 1 shifts the function left 2 and down 1, thus the axis of symmetry is x = -2