Question

Which functions have an axis of symmetry of x = –2? Check all that apply.

f(x) = x2 + 4x + 3
f(x) = x2 – 4x – 5
f(x) = x2 + 6x + 2
f(x) = –2x2 – 8x + 1
f(x) = –2x2 + 8x – 2

Answer 1

Use the vertex formula x = -b/(2a). For an axis x = -2 we need -b/(2a) = -2, i.e. b = 4a.

Check:
- x^2 + 4x + 3: a=1, b=4 → 4 = 4·1 — yes.
- x^2 – 4x – 5: a=1, b=-4 → no.
- x^2 + 6x + 2: a=1, b=6 → no.
- -2x^2 – 8x + 1: a=-2, b=-8 → -8 = 4·(-2) — yes.
- -2x^2 + 8x – 2: a=-2, b=8 → no.

So the 1st and 4th functions have axis x = -2.