Question

what is the focus of the parabola
$y = - \frac{1}{4} {x}^{2} - 2x - 2$
enter your answer in the Box

I've seen so many wrong answers and I got it wrong on my quiz

answer: (-4,1)​

Answer 1

Answer:

(-4,1)

Step-by-step explanation:

The given parabola is

$y = - \frac{1}{4} {x}^{2} - 2x - 2$

When we rewrite in vertex form, we get;

$y = - \frac{1}{4} {(x + 4)}^{2} + 2$

Or

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

When we compare to:

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

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)