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Solution

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Solution Steps

Step 1: Identify the Key Points on the Graph
  • The graph shows a polynomial function with key points at approximately (-20, -12), (-10, 8), (0, 0), (10, -8), and (20, 0).
Step 2: Determine the Degree of the Polynomial
  • The graph has three turning points, indicating that the polynomial is of degree 4 (since a polynomial of degree n can have up to n-1 turning points).
Step 3: Analyze the Behavior at Key Points
  • The polynomial crosses the x-axis at x = -20, 0, and 20.
  • The local maximum is at approximately (-10, 8).
  • The local minimum is at approximately (10, -8).

Final Answer

The polynomial function is of degree 4 with key points at approximately (-20, -12), (-10, 8), (0, 0), (10, -8), and (20, 0).

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