SOLUTION: (x-1)2=(12y-1).This is a 6 answer question my son is having trouble with. we need to find the: 1]vertex 2]focus 3]axis of symmetry 4]directrix 5]direction 6]length of latus r

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: (x-1)2=(12y-1).This is a 6 answer question my son is having trouble with. we need to find the: 1]vertex 2]focus 3]axis of symmetry 4]directrix 5]direction 6]length of latus r      Log On


   

Question 44940: (x-1)2=(12y-1).This is a 6 answer question my son is having trouble with. we need to find the:
1]vertex
2]focus
3]axis of symmetry
4]directrix
5]direction
6]length of latus rectum
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
%28x+-+1%29%5E2+=+12y+-+1
%28x+-+1%29%5E2+%2B+1+=+12y
%281%2F12%29%28x+-+1%29%5E2+%2B+1%2F12+=+y This Is Called Vertex Form
Vertex Form: a%28x+-+h%29+%2B+k+=+y
1]vertex
(h,k)
(1,1/12)
3]axis of symmetry
Since the parabola is vertical, the axis of symmetry is vertical and goes through the vertex: x+=+1
2]focus
Now: 'p' is the distance from the vertex to foci as well as the distance from the vertex to the directrix
p+=+1%2F%284a%29
p+=+1%2F%284%281%2F12%29%29
p+=+1%2F%281%2F3%29
p+=+3
3 units above the vertex: (1,3 1/12) or (1,37/12)
4]directrix
opposite of 'p'
3 units below the vertex; also, the directrix is a horizontal line: y+=+-37%2F12
5]direction
We know that the parabola is vertical because 'x' is square, not 'y'. Since the value known as 'a' is positive, your parabola opens upward.
6]length of latus rectum
The Latus Rectum is the distance from one point of the parabola to the other going through the focus (in a straight line.)
LR = |1/a|
LR = |1/(1/12)|
LR = 12