Question

Find the focus. y= -1/12 (x)² - 6

Answer 1

Answer:

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

Step-by-step 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

   $(h,k+\dfrac{1}{4a})$

Here, the equation is

   $y=-\dfrac{1}{12}x^2-6$

so

   $a=-\dfrac{1}{12}\\\\h = 0\\\\k =-6$

So,

$k+\dfrac{1}{4a}=-6-\dfrac{12}{4}=-6-3=-9$

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