Question

Identify the vertex, focus, and directrix.
y=(1/12)(x^2)

Answer 1

Ok so the normal equation of a parabola is \[y^2=4ax\]
Which would be for a horizontal parabola with the focus on the x axis

However the x^2 tells us that the parabola is U shaped so the focus is on the y axis
Rearrange to the form x^2 = 4ay

x^2 = 12y

From this we can see that a= 3

Focus of this parabola is on the y axis so is at (0,a) = (0,3)
Directrix y= -a y=-3

Parabola is centred on (0,0) So vertex is just that.