Question 44940
{{{(x - 1)^2 = 12y - 1}}}
{{{(x - 1)^2 + 1 = 12y}}}
{{{(1/12)(x - 1)^2 + 1/12 = y}}} This Is Called Vertex Form
Vertex Form: {{{a(x - h) + 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/(4a)}}}
{{{p = 1/(4(1/12))}}}
{{{p = 1/(1/3)}}}
{{{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 = -37/12}}}
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
{{{ graph( 600, 600, -10, 10, -10, 10, (1/12)(x - 1)^2 + 1/12,-37/12) }}}