y=2x^2 has vertex at the origin (0,0). It's an upward opening parabola, with focus above and directrix below the vertex. Line of symmetry is x=0

The focus has x coordinate = 0, (0,a), where y=(1/4a)x^2. 2 = 1/4a, a = 1/8. focus is (0, 1/8) and directrix is y=-1/8. Points on the parabola are equidistant to the focus and directrix. the point (1/4, 1/8) is on the parabola, y=2(1/4)^2 = 1/8 It's a distance 1/4 to the focus and 1/4 to the directrix.