1. **State the problem:** Determine the domain and range of a parabola that opens upwards with vertex at approximately $(-3,-2)$. 2. **Recall the properties of a parabola:** - The vertex form of a parabola is given by $$y = a(x-h)^2 + k$$ where $(h,k)$ is the vertex. - Since the parabola opens upwards, $a > 0$. - The domain of any parabola is all real numbers because it extends infinitely left and right. 3. **Domain:** - The parabola extends infinitely in the $x$-direction, so the domain is $$\text{Domain} = (-\infty, \infty)$$. 4. **Range:** - Since the parabola opens upwards and the vertex is the minimum point at $y = -2$, the range is all $y$ values greater than or equal to $-2$. - Thus, $$\text{Range} = [-2, \infty)$$. 5. **Summary:** - Domain: all real numbers. - Range: $y \geq -2$. This matches the description of the parabola centered at $x = -3$ with vertex $(-3,-2)$ opening upwards.