Question

Help plz i’m unsure how to do this. Plato

Answer 1

C

Explanation:

Standard form of a Parabola that facing downwards, with focus, p and vertex (h,k)

`- (x - h) {}^(2) = 4p(y - k)`

We know the vertex is (-4,-3) so we get

`- (x - ( - 4) {}^(2) = 4p(y - ( - 3)`

`- (x + 4) {}^(2) = 4p(y + 3)`

Now we need to find the length of the focus.

The focus length is 1 because the distance from the vertex to focus is 1 so p=1

`- (x + 4) {}^(2) = 4(y + 3)`

`- ( {x}^(2) + 8x + 16) = 4y + 12`

`- {x}^(2) - 8x - 16 = 4y + 12`

`- {x}^(2) - 8x - 28 = 4y`

`\frac{ - {x}^(2) }{4} - 2x - 7 = y`

C is the answer