You provided the function \( f(t) = t^2 + 9 \). If you're looking for more insights or operations to perform with this function, here are a few possibilities:

1. **Evaluate the function at a specific point**: For example, you can find \( f(2) \) by substituting \( t = 2 \).
2. **Find the derivative**: The derivative of \( f(t) \) with respect to \( t \) will give the rate of change of the function.
3. **Find the second derivative**: This would give the curvature or concavity of the graph.
4. **Find critical points**: Solve \( f'(t) = 0 \) to find potential maximum, minimum, or saddle points.
5. **Graph the function**: Visualize how \( f(t) = t^2 + 9 \) looks. It's a parabola shifted 9 units up.

Would you like to explore any of these operations or have any other questions?

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Here are 5 related questions:

1. What is the value of \( f(t) \) when \( t = 3 \)?
2. How do you find the derivative of \( f(t) = t^2 + 9 \)?
3. What is the nature of the graph of \( f(t) = t^2 + 9 \)?
4. At what points does the function \( f(t) = t^2 + 9 \) have a minimum value?
5. What is the second derivative of \( f(t) \)?

**Tip**: The function \( f(t) = t^2 + 9 \) is always positive, since \( t^2 \) is non-negative and you're adding 9.

Explore the quadratic function f(t) = t^2 + 9. Learn how to evaluate, differentiate, and graph this function, and find critical points. This problem involves derivatives, graphing, and analyzing parabolas. Suitable for students in Grades 9-12.

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