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).

goog may have it for you

x=17

step-by-step explanation:

solve 3x-24=x+10

then that makes it 2x=34 because you subtract an x from both sides to get rid of the one on the right, and then you add 24 to both sides to get rid of the 24 on the left

divide by both sides by 2 to get your answer so that you can get your answer