To determine the absolute maximum and minimum points on the graph:

Observing the Graph:

1. The curve reaches its highest point (absolute maximum) at the top of the parabola, where $x = -2$ and $y = 5$. Thus, the absolute maximum is at $(-2, 5)$.

2. The curve reaches its lowest point (absolute minimum) at the rightmost endpoint, where $x = 4$ and $y = -5$. Thus, the absolute minimum is at $(4, -5)$.

Final Answer:

• Absolute Maximum: $(-2, 5)$
• Absolute Minimum: $(4, -5)$

Let me know if you'd like further clarification or a deeper explanation! Here are some questions to expand your understanding:

1. How can we determine local extrema versus absolute extrema?
2. What methods can be used to find extrema algebraically for given functions?
3. How do endpoints influence the determination of absolute extrema?
4. What is the significance of critical points on graphs in identifying extrema?
5. How would the graph change if it represented a function with a larger domain?

Tip: Always evaluate the endpoints of a graph or function when searching for absolute extrema!