Parabolas!

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--Hope everyone had a safe/blessed day! (:

-Only have x^2 or y^2, not both
-Axis of symmetry: x=-b/2a
-Vertex: (-b/2a, f(-b/2a))
-Focus:
1. Find p using the formula: 1/4p=coeff of leading term
2. Vertex coordinate +p=your focus if it is x^2, you add the y coordinate of the vertex and vise versa.
3. Put in point form

--Standard Form: y+h=a(x+k)
Vertex(k,-h)
a-leading coeff.

Directrix:
1. Find p (see above)
2. Vertex coordinate -p=directrix
3. Write as y=number

Example 1:
For each parabola give the coordinates of its vertex and focus and the equation of its directrix.
y=1/8x^2
x=-0/2(1/8)
x=0
vertex: 1/8(0)^2
(0,0)
1/4p=1/8
p=2
0+2=2
(0,2)
0-2=-2
y=-2

Example 2:
For each parabola give the coordinates of its vertex and focus and the equation of its directrix.
x=1/8y^2
y=0/2(1/8)
y=0
vertex: 1/8(0)^2
(0,0)
1/4p=1/8
p=2
0+2=2
(2,0)
0-2=-2
x=-2

Example 3:
For each parabola give the coordinates of its vertex and focus and the equation of its directrix.
y=-1/12x^2
x=0/2(-1/2)
x=0
Vertex: -1/12(0)^2
(0,0)
1/4p=-1/12
-4p=12
p=-3
0+-3=-3
(0,-3)
0+3=3
y=3