Question

What is the vertex of `y= -(x+2)^2-2x^2-x-4`?

Answer 1

Vertex is `(-5/6,-71/12)`

Explanation:

`y=-(x+2)^2-2x^2-x-4`

= `-(x^2+4x+4)-2x^2-x-4`

= `-3x^2-5x-8`

= `-3(x^2+5/3x+(5/6)^2)-(-3)(5/6)^2-8`

= `-3(x+5/6)^2+25/12-8`

= `-3(x+5/6)^2-71/12`

Now it is in vertex form `y=a(x-h)^2+k`

and vertex is `(-5/6,-71/12)`

graph{-(x+2)^2-2x^2-x-4 [-6.876, 3.124, -8.7, -3.7]}