State the vertex of the function, \( g(x)=(x+2)^{2}-1 \) \( (2,1) \) \( (-2,-1) \) \( (-2,1) \) \( (-2,-1) \)

The vertex of the function \( g(x)=(x+2)^{2}-1 \) can be found directly from its vertex form, which is \( g(x) = a(x-h)^2+k \). Here, \( h = -2 \) and \( k = -1 \). This tells us that the vertex is at the point \((-2, -1)\). Isn't it fascinating that this type of function, known as a parabola, always has its vertex as either the highest or lowest point? Whether it's opening upwards like this one or downwards, parabolas truly create unique U-shaped paths that can represent various real-world scenarios, from projectile motion to the design of parabolic reflectors!