Step 1 :The function \(f(x)=(x+2)^{2}-3\) is in the form \(f(x)=(x-h)^{2}+k\), where \((h,k)\) is the vertex of the parabola.
Step 2 :In this case, the vertex is at \((-2,-3)\).
Step 3 :The parabola opens upwards because the coefficient of \((x+2)^{2}\) is positive.
Step 4 :The graph of the function \(f(x)=(x+2)^{2}-3\) is a parabola that opens upwards with its vertex at \((-2,-3)\).
Step 5 :\(\boxed{\text{Final Answer: The graph of the function } f(x)=(x+2)^{2}-3 \text{ is a parabola that opens upwards with its vertex at } (-2,-3)}\)