Answer:
1. C, E, G
2. A, D, H
Step-by-step explanation:
Compare each equation to the form ...
f(x) = 1/(4p)(x -h)^2 +k
In this form, p is the distance from the vertex to the focus (positive is up), and (h, k) is the location of the vertex. The focus is (h, k+p); the directrix is y=k-p.
1. The equation tells us ...
(h, k) = (1, 4)
1/(4p) = (-1) . . . ⇒ . . . p = -1/4
So, we have ...
- vertex: (1, 4) . . . . . . . . (G)
- focus: (1, 3 3/4) . . . . . (C)
- directrix: y=4 1/4 . . . . (E)
--
2. The equation tells us ...
(h, k) = (-1, 4)
1/(4p) = 2 . . . ⇒ . . . p = 1/8
So, we have ...
- vertex: (-1, 4) . . . . . . . . (A)
- focus: (-1, 4 1/8) . . . . . . (H)
- directrix: y = 3 7/8 . . . (D)
