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

Explanation:

Step1: Recall vertex form axis of symmetry

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where the axis of symmetry is \( x = h \).

Step2: Analyze each function

• For \( f(x)=(x - 1)^2+2 \), comparing with \( a(x - h)^2 + k \), \( h = 1 \), so axis of symmetry is \( x = 1 \).
• For \( f(x)=(x + 1)^2-2=(x - (-1))^2-2 \), \( h=- 1 \), axis of symmetry is \( x=-1 \).
• For \( f(x)=(x - 2)^2-1 \), \( h = 2 \), axis of symmetry is \( x = 2 \).
• For \( f(x)=(x + 2)^2-1=(x - (-2))^2-1 \), \( h=-2 \), axis of symmetry is \( x=-2 \).

Answer:

\( f(x)=(x + 2)^2 - 1 \)