Question

Find the focus. y= -1/12 (x)² - 6

Answer 1

`\Large \boxed{\sf\ \ (0,-9) \ \ }`

Explanation:

Hello,

We know that when the parabola equation is

`y=a(x-h)^2+k`

the vertex is (h,k) and the focus is

`(h,k+(1)/(4a))`

Here, the equation is

`y=-(1)/(12)x^2-6`

so

`a=-(1)/(12)\\\\h = 0\\\\k =-6`

So,

`k+(1)/(4a)=-6-(12)/(4)=-6-3=-9`

Then, the focus is

`\large \boxed{\sf\ \ (0,-9) \ \ }`

I attached the graph, included the focus so that you can see it :-)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you