Answer:
(-4,1)
Step-by-step explanation:
The given parabola is
[tex]y = - \frac{1}{4} {x}^{2} - 2x - 2[/tex]
When we rewrite in vertex form, we get;
[tex]y = - \frac{1}{4} {(x + 4)}^{2} + 2[/tex]
Or
[tex]{(x + 4)}^{2} = - 4( y - 2)[/tex]
When we compare to:
[tex]{(x - h)}^{2} = 4p( y - k)[/tex]
We have 4p=-4
This means p=-1
But the vertex is at:
(-4,2)
Since it is a vertical parabola that opens down, the focus is one unit(|p|=1) below the vertex.
Hence the focus is (-4,1)
