The vertex of this equation is (-3, -13)
You can find any vertex by first looking for the x value. You can find the x value by using the following equation.
-b/2a
In this equation, 'a' refers to the coefficient of x^2 (1) and 'b' refers to the coefficient of x (6). So we can use these numbers to find the x value.
-b/2a
-(6)/2(1)
-6/2
-3
Now that we have the x value, we can substitute the value in for x and solve for the y value.
x^2 + 6x - 4
(-3)^2 + 6(-3) - 4
9 - 18 - 4
-13
And this gives you the ordered pair of (-3, -13)