#### Answer

minimum: $(-1,-7)$

#### Work Step by Step

We are given:
$g(x)=2x^{2}+4x-5$
We factor by completing the square:
$2(x^{2}+2x)-5$
$2(x^{2}+2x+1)-5-2$
$2(x+1)^{2}-7$
We see that this is a transformed parabola: $x^2$ moved left 1 unit and down 7 units. Thus the minimum would occur at $(-1,-7)$.