Question

What is the vertex of `y= -3x^2 + 12x +6`?

Answer 1

The vertex is `(2,18)`

Explanation:

`y=-3x^2+12x+6`
Differentiating with respect to x
`dy/dx=-6x+12`
Any max or min is when `dy/dx=0`
`-6x+12=0 => 6x=12 => x=2`
To determine if it's a max or min , we must differentiate once more
So `(d^2y)/(dx^2)=-6` (<0)
so it's a maximum
The vertex is when `x=2` and `y=-3*2*2+12*2+6 =-12+24+6=18`
Here is a graph of the function

graph{-3x^2+12x+6 [-40, 40, -20, 20]}