1. **Problem 4:** Given a quadratic function graph with vertex, zeros, minimum value, and axis of symmetry to find. 2. The vertex of a quadratic function in standard form $y = ax^2 + bx + c$ is given by the formula $$\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$$ but here it is directly read from the graph as $(-1, -3)$. 3. The minimum value of the function is the $y$-coordinate of the vertex since the parabola opens upwards, so minimum value is $-3$. 4. The zeros of the function are the $x$-intercepts where $g(x) = 0$. From the graph, zeros are approximately $-3$ and $1$. 5. The axis of symmetry is the vertical line passing through the vertex, so it is $x = -1$. 6. **Problem 5:** Jeremiah's altitude after 2 seconds diving is modeled by $$d(x) = \frac{1}{2}x^2 - 10x$$. 7. Substitute $x=2$: $$d(2) = \frac{1}{2} \times 2^2 - 10 \times 2 = \frac{1}{2} \times 4 - 20 = 2 - 20 = -18$$ So, his altitude after 2 seconds is $-18$ meters. 8. **Problem 6:** Domain and range of the quadratic function part shown in the top-right graph. 9. The domain of any quadratic function is all real numbers, so domain is $(-\infty, \infty)$. 10. The range depends on the vertex and parabola direction. Since it opens upwards and vertex is at $y = -3$, the range is $$[-3, \infty)$$. **Final answers:** - Vertex: $(-1, -3)$ - Minimum value: $-3$ - Zeros: $-3$ and $1$ - Axis of symmetry: $x = -1$ - Altitude after 2 seconds: $-18$ meters - Domain: $(-\infty, \infty)$ - Range: $[-3, \infty)$