1. The problem asks which function has a minimum at the point $(-2, -3)$. 2. The vertex form of a quadratic function is given by $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex (minimum or maximum point). 3. Since the minimum is at $(-2, -3)$, the vertex form must be $$y = a(x - (-2))^2 + (-3) = a(x + 2)^2 - 3$$. 4. Now, check the options: - A: $y = (x - 2)^2 - 3$ has vertex $(2, -3)$, not $(-2, -3)$. - B: $y = (x - 2)^2 + 3$ has vertex $(2, 3)$, not $(-2, -3)$. - C: $y = (x + 2)^2 + 3$ has vertex $(-2, 3)$, not $(-2, -3)$. - D: $y = (x + 2)^2 - 3$ has vertex $(-2, -3)$, which matches the required minimum point. 5. Therefore, the function with a minimum at $(-2, -3)$ is option D: $$y = (x + 2)^2 - 3$$.