Answer
$y = -11.125$
Work Step by Step
The vertex form of a quadratic function is
$y = a(x-h)^2+k$, where $(h,k)$ is the vertex.
Since the coefficient of $x^2$ is $2$, $a$ must be equal to 2.
$y = 2(x-h)^2 + k$
If we divide the right side of the function by $2$, we will get $x^2 + 2.5x-4$.
Try to make this a perfect square.
$(x^2+2.5x + 1.25^2) - 1.25^2 -4$
$(x+1.25)^2 - 1.5625 - 4$
$(x+1.25)^2 - 5.5625$
Multiply this by $2$ to get the right side of the function.
$y = 2(x+1.25)^2 -11.125$
The coordinates of the vertex are $(-1.25,\boxed{-11.125})$
