What is the focus of the parabola? y=−1/4x2−2x−2

The focus is (-4, 1).

Step-by-step explanation:

y = −1/4x2 − 2x − 2

We convert this to the form (x - h)^2  = 4p(y - k)  where p is the distance  between the vertex and the focus, h and k are the coordinates of the vertex.

Fist we multiply the equation by -4 so as to make the coefficient of x^2 = 1.

-4y = x^2 + 8x + 8

Now we need to make the right side a perfect square.

We do this by adding 8 to both sides:

-4y + 8 = x^2 + 8x + 16

-4(y - 2) = (x + 4)^2

(x + 4)^2 = -4((y - 2)

Comparing this with the standard form:

(x - h)^2  = 4p(y - k)  

4p = -4

so p = -1.

Now the vertex (h, k) is (-4, 2).

This parabola opens downwards because of the -1/4 before the x^2 so the

focus is. (h, k + p) = (-4,2-1)

= (-4, 1).

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation: