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

Answer:The focus is (-4, 1).Step-by-step explanation:y = −1/4x2 − 2x − 2We 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 + 8Now 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 thefocus is. (h, k + p) = (-4,2-1)= (-4, 1).