Question

The graph of which function has an axis of symmetry at x = one-quarter?

f(x) = 2x2 + x – 1
f(x) = 2x2 – x + 1
f(x) = x2 + 2x – 1
f(x) = x2 – 2x + 1

Answer 1

For a quadratic ax^2+bx+c the axis of symmetry is x = -b/(2a). Set -b/(2a) = 1/4 → b = -a/2.

Check the choices:
- 2x^2 + x – 1: -b/(2a) = -1/(4) = -1/4 (no)
- 2x^2 – x + 1: -(-1)/(2·2) = 1/4 (yes)
- x^2 + 2x – 1: -2/(2·1) = -1 (no)
- x^2 – 2x + 1: -(-2)/(2·1) = 1 (no)

Answer: f(x) = 2x^2 – x + 1.