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## Sagot :

**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