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.