Asked by T
The equation of a parabola is 12y=(x-1)^2-48. Identify the vertex, focus, and directrix of the parabola.
Answers
Answered by
oobleck
the parabola x^2 = 4py has
vertex at (0,0)
focus at (0,p)
directrix at y = -p
So. Let's rearrange things a bit.
12y=(x-1)^2-48
(x-1)^2 = 12(y+4)
So, we can see that we now have
vertex at (1,-4)
focus at y=(-4+3) = (1,-1)
directrix at y=(-4-3) or y = -7
to confirm our work, see
https://www.wolframalpha.com/input/?i=parabola+12y%3D(x-1)%5E2-48
vertex at (0,0)
focus at (0,p)
directrix at y = -p
So. Let's rearrange things a bit.
12y=(x-1)^2-48
(x-1)^2 = 12(y+4)
So, we can see that we now have
vertex at (1,-4)
focus at y=(-4+3) = (1,-1)
directrix at y=(-4-3) or y = -7
to confirm our work, see
https://www.wolframalpha.com/input/?i=parabola+12y%3D(x-1)%5E2-48
Answered by
henry2,
12y = (x-1)^2 - 48.
Vertex form: Y = a(x-h)^2 + k.
Y = (1/12)(x-1)^2 - 4.
V(h, k) = V(1, -4).
F(h, k+1/(4a)) = F(1, -1).
D(h, k-1/(4a)) = D(1, -7).
Vertex form: Y = a(x-h)^2 + k.
Y = (1/12)(x-1)^2 - 4.
V(h, k) = V(1, -4).
F(h, k+1/(4a)) = F(1, -1).
D(h, k-1/(4a)) = D(1, -7).
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.