Question

Sketch the graph and find following info:
Vertex:
Focus:
Directrix:
Axis of Symmetry:
Ends of Latus Rectum:

(x-2)^2=4(y-3)

I think the vertex is (2,3) is this correct, and how do I proceed on?

Thank you!

Answer 1

(x-2)^2 = 4(y-3).

(x-2)^2 = 4y - 12,
(x-2)^2 + 12 = 4y,
Divide both sides by 4:
y = 1/4(x-2)^2 +3, Vertex Form.

V(h,k) = (2,3).

a = 1/4.
4a = 1.

F(2,Y2). Y2 = k + 4a = 3 + 1 = 4.

V(2,3)

D(2,Y1). Y1 = k-4a = 3 - 1 = 2.

Axis: x = 2.

Use the following points for graphing:

(0,4), (1,1/4), V(2,3), (3,1/4), (4,4).