Graph ​ g(x)=−2x^2−12x−24 ​.

The x coordinate of the vertex is given by    - (-12) / (2 * - 2)  =  12/ -4  = - 3

Putting this back into the function to get the y coordinate of the vertex we have

-2(-3)^2 - 12(-3) - 24  =   

-18 + 36 - 24 = 

- 6

So....the vertex is  (-3, -6)

And we can find another point by letting x = 0

-2(0)^2 - 12(0)  - 24 =

-24

So...the second point is  (0, -24)

Here's the graph :  https://www.desmos.com/calculator/synw1wfvuo

thank you