graph the function h(t) = -0.2t4 + 4t3 - 24t2 + 48t

Here is the graph of the function \( h(t) = -0.2t^4 + 4t^3 - 24t^2 + 48t \). You can observe the general shape and key points of the curve. 

Would you like any further details or explanations about the graph?

Here are 5 related questions you can explore:
1. What are the local maximum and minimum points of this function?
2. At what values of \( t \) does \( h(t) = 0 \) (the roots of the equation)?
3. What is the behavior of the function as \( t \to \infty \) or \( t \to -\infty \)?
4. How can you find the inflection points of this function?
5. How does the degree of the polynomial influence the shape of the graph?

**Tip:** For analyzing polynomials, focus on both end behavior and critical points to understand their full behavior.

Graph the function h(t) = -0.2t^4 + 4t^3 - 24t^2 + 48t

Explore the graph of the polynomial function h(t) = -0.2t^4 + 4t^3 - 24t^2 + 48t, learn how to find critical points, and understand end behavior. This problem introduces key concepts in polynomial graphing and is suitable for students in Grades 10-12.

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