Find the vertex, focus, and directix of this parabola. Graph the equation. x^2 = 4y

Question

Find the vertex, focus, and directix of this parabola. Graph the equation.
x^2 = 4y

Vertex
( , )
Focus
( , )
Directix
=

Answer 1

4y= x^2

y = (1/4)x^2

it's an upward opening parabola, minimum point = vertex = the origin (0,0)

focus has x coordinate = 0 and y coordinate >0

directrix is y = a constant less than 0

focus is (0,1), directrix is y=-1, vertex (0,0) is midway between them

point (2,1) is on the parabola, which is 2 units from the focus

and also 2 units from the directrix

it might help to sketch the parabola