Question

What is the vertex of `y=2(x +3)^2 -8x`?

Answer 1

The vertex is `(-1,16)`.

Explanation:

In order to know, we will develop first, it will make the next calculus easier.

`y = 2x^2 + 12x + 18 - 8x = 2x^2 + 4x + 18`. The coefficient of `x^2` is positive so we know the vertex is a minimum. This vertex will be the zero of the derivative of this trinomial. So we need its derivative.

`f(x) = 2x^2 + 4x + 18` so `f'(x) = 4x + 4 = 4(x+1)`. This derivative is zero for `x = -1` so the vertex is at the point `(-1,f(-1)) = (-1,16)`