The equation of a parabola is 12y=(x1)248 identify the vertex, focus, and directrix of the parabola?

I just really do not understand this. Please help and explain! Thank you!

1 Answer
May 17, 2018

The vertex form of the equation of a parabola that opens up or down is:

y=a(xh)2+k

In this form, we can easily identify the vertex as the point (h,k). Using the formula, f=14a, allows us to determine the focus:

(h,k+f)

and the equation of the directrix:

y=kf

I shall apply this general information to your problem.

Given: 12y=(x1)248

We can make the given equation match the vertex form by dividing both sides of the equation by 12:

y=112(x1)24

We can easily identify the vertex as (h,k)=(1,4)

We observe that a=112 and we use the formula to compute f:

f=14a

f=14(112)

f=3

We can determine the focus:

(h,k+f)=(1,4+3)

(h,k+f)=(1,1)

We can write the equation of the directrix:

y=kf

y=43

y=7