Answer:
Vertex = (-4,-5)
P-value = -2
Opens Downward
Step-by-step explanation:
Given:
- Focus = (-4,-7)
- Directrix = -3
Since focus is less than directrix, the parabola obviously opens downward.
To find vertex (h,k), for downward parabola, focus is (h, k + p) and directrix is y = k - p
We have:
[tex]\displaystyle \large{k+p=-7 \to (1)}\\\displaystyle \large{k-p=-3 \to (2)}[/tex]
First equation being focus and second being directrix, solve the simultaneous equation:
[tex]\displaystyle \large{2k=-10}\\\displaystyle \large{k=-5}[/tex]
Substitute k = -5 in any equation - I’ll choose (1) for this:
[tex]\displaystyle \large{-5+p=-7}\\\displaystyle \large{p=-2}[/tex]
Therefore vertex is at (h,k) = (-4,-5) with p-value being -2 since p < 0 then the parabola opens downward.
Attachment added for visual reference
