1. Vertex form (standard form) for the equation of a parabola
y = a(x – h)2 + k x = a(y – k)2 + h
Vertex: (h, k) Vertex: (h, k)
Line of symmetry: x = h Line of symmetry: y = k

2. Graph x = 2y2 + 8y + 9
x = (2y2 + 8y )+9
x = 2(y2 + 4y + 4) + 9 - 8
x = 2(y + 2)2 + 1
Vertex: (1, -2)
Axis of symmetry: y = -2
Opens to the right

3. focus
directrix

4. latus rectum
directrix

5. y = a(x – h)2 + k
focus
1
same distance
4a
directrix
latus rectum

6. y = a(x – h)2 + k
focus
latus rectum
length
1
directrix
a

7. Pg 422

8. 4(y – 2) = (x + 3)2 y = a(x – h)2 + k
4y – 8 = (x + 3)2
4y = (x + 3)2 + 8
4 4
y = ¼ (x + 3)2 + 2
a=¼
h = -3
k=2

10. y = ¼ (x + 3)2 + 2
vertex: (-3, 2)
axis of symmetry:
x = -3
a=¼
distance from vertex
1_
to focus = 4(¼) = 1
Length of latus
distance from vertex rectum:
to directrix = 1
1 = 4 units
¼

11. 4x – 13 = y2 – 2y x = a(y – k)2 + h
4x – 13 = (y2 – 2y +1) – 1
+13 +13
4x = (y – 1)2 + 12
4 4
x = ¼ (y – 1)2 + 3

12. x = ¼ (y – 1)2 + 3
vertex: (3, 1)
axis of symmetry:
y=1
a=¼
distance from vertex
1_
to focus = 4(¼) = 1
Length of latus
distance from vertex rectum:
to directrix = 1
1 = 4 units
¼