Consider the following points.
(−2, 28), (−1, 0), (0, −6), (1, −8), (2, 0)
(a) Determine the polynomial function of least degree whose graph passes through the given points.
p(x) =

(b) Sketch the graph of the polynomial function, showing the given points.

Here is the graph of the polynomial function \( p(x) = x^4 - x^3 + x^2 - 3x - 6 \). The red points on the graph correspond to the given points \((-2, 28)\), \((-1, 0)\), \((0, -6)\), \((1, -8)\), and \((2, 0)\).

Would you like more details on how this graph was constructed or have any other questions?

Here are some related questions you might find useful:
1. What is the general form of a polynomial of degree \( n \)?
2. How do you determine the degree of a polynomial based on given points?
3. What are the roots of the polynomial \( p(x) = x^4 - x^3 + x^2 - 3x - 6 \)?
4. How can you use interpolation to find a polynomial function?
5. What is the significance of the leading coefficient in a polynomial function?
6. How does the degree of a polynomial affect the shape of its graph?
7. What are the key features of the graph of a polynomial function?
8. How do you determine if a polynomial function has symmetry?

**Tip:** When finding a polynomial function from points, always check if the number of points corresponds to the degree of the polynomial you're solving for.

Explore the graph of a polynomial function that passes through points (-2, 28), (-1, 0), (0, -6), (1, -8), (2, 0). Understand how to determine the polynomial function using interpolation methods. Suitable for high school students studying polynomial functions and interpolation.

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