The graph of which function has an axis of symmetry at x = 3? f (x) = x2 3x 1 f (x) = x2 - 3x - 3 f (x) = x2 6x 3 f (x) = x2 - 6x - 1

A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.

f (x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2) ^2 - 5/4 = > vertex = (-3/2, - 5/4)

f (x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2) ^2 - 21/4 = > vertex = (3/2, - 21/4)

f (x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3) ^2 - 6 = > vertex = (-3, - 6)

f (x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3) ^2 - 10 = > vertex = (3, - 10)

Therefore, f (x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.