a)

y = -(1/4)(x - 2)^2 + 5

y - 5 = (-1/4)(x - 2)^2 multiply through by 4

4(y - 5) = -(x - 2)^2

The vertex is ( 2, 5)

4p = 4

p = 1

This parabola turns downward

The focus is (2, 5 - p) = (2, 5 - 1) = (2, 4)

The directrix is y = 5 + p = 5 + 1 = 6 ⇒ y = 6