Vertex is 1 unit away from either focus or directrix. Vertex a maximum.
VERTEX ---
FOCUS ---
DIRECTRIX y=0
L.R. 4
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vertex is at point(0,-1);
focus at (0,-2), one unit downward from vertex Answer by ikleyn(52873) (Show Source): You can put this solution on YOUR website! .
I am here to fix the errors of the @josgarithmetic solution.
The parabola is downward.
Vertex is a maximum. It is (0,-1).
FOCUS is (0,-2) one unit down from the vertex
DIRECTRIX is y= 0. one unit up from the vertex
L.R. is 4 the wide of the parabola at the focus level
A bit of further explanation of where the answers come from -- in case you aren't familiar with it....
The vertex form of the equation of a parabola that opens up or down is
or
In this form, the vertex is (h,k), and p is the directed distance from the directrix to the vertex and from the vertex to the focus. Furthermore, |4p| is the length of the latus rectum.
In this problem, the equation in that form is
or
This is in vertex form; (h,k) = (0,-1), and 4p = -4 so p = -1.
Then the directed distance from the directrix to the vertex is -1, which makes the directrix y=0; and the directed distance from the vertex to the focus is -1, which makes the focus (0,-2).
And finally the length of the latus rectum is |4p| = |-4| = 4.