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To analyze the given polynomial graph \( p(x) \), we need to identify the number of turning points and roots.

### Turning Points
Turning points are points where the graph changes direction from increasing to decreasing or vice versa. These points are also where the first derivative of the polynomial \( p'(x) \) is zero.

By observing the graph:
1. The graph has a turning point between \(-2\) and \(-1\) (a local maximum).
2. The graph has another turning point between \(-1\) and 0 (a local minimum).
3. The graph has a turning point between 0 and 1 (a local maximum).
4. The graph has a turning point between 1 and 2 (a local minimum).

Thus, there are **4 turning points**.

### Roots (Zeros)
Roots of the polynomial are the points where the graph intersects the x-axis.

By observing the graph:
1. There is a root at \( x = -1 \).
2. There is a root at \( x = 0 \).
3. There is a root at \( x = 2 \).

Thus, there are **3 roots**.

### Summary
- Number of turning points: **4**
- Number of roots: **3**

Would you like any more details or have any questions?

Here are some related questions you might find useful:
1. How to find the degree of a polynomial based on its graph?
2. What are the possible shapes of polynomial graphs?
3. How do turning points relate to the degree of a polynomial?
4. How to find the exact coordinates of turning points?
5. How to determine the concavity of a polynomial graph?

**Tip:** To identify the degree of a polynomial, remember that the number of turning points is at most \( n-1 \) where \( n \) is the degree of the polynomial.

Explore the analysis of polynomial graphs to identify turning points and roots. This problem highlights key concepts such as the conditions for turning points (4 total) and the roots (3 total) of the polynomial. Ideal for high school students studying calculus.

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