Respuesta :
Answer:
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).
Answer: Just took the test the guy above me is correct
Step-by-step explanation:
