The document provides instructions to find the vertex, focus, and directrix of the parabolic equation (x-1)^2 = 4(y-2). The vertex is located at point (1,2), the focus is above the vertex at (1,3), and the directrix is below the vertex along the line y=1.

1. Find the vertex, focus, and directrix of the parabola. Graph the equation.
(x-1)^2 = 4(y-2)
Solution
(x-1)^2 = 4(y-2)
Std form : (x - h)2 = 4p(y - k)
Vertex ( h, k) ----> ( 1 , 2)
This is an upward facing parabola:
Now 4p = 4 ---> p =1
Vetex is at ( 1,2), so focus would be above the vertex on x=1 by 1 unit .i.e. (1, 3)
The directrix is equidistant from the vertex that the focus is.: so, it is below the vertex by same
distnace focus is above it : y = 1