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Given Information:

The equation provided is $f(x) = (x - 2)(x + 4)(x - 3)$. The goal is to find several characteristics of this polynomial:

1. X-Intercepts: The roots of the polynomial are already calculated as:

   • $x = 2, -4, 3$ (from solving $f(x) = 0$).

2. Y-Intercept: To find the $y$-intercept, substitute $x = 0$ into $f(x)$: $f(0) = (0 - 2)(0 + 4)(0 - 3) = (-2)(4)(-3) = 24$ So, the $y$-intercept is $(0, 24)$.

3. Degree of Polynomial: The degree of the polynomial is determined by the highest power of $x$ when expanded. Here, $f(x)$ has three linear factors ($(x - 2), (x + 4), (x - 3)$), so the degree is: $\text{Degree} = 3$

4. End Behavior: Since this is a cubic polynomial (odd degree) with a positive leading coefficient (from $x^3$), the end behavior is:

   • As $x \to -\infty$, $f(x) \to -\infty$.
   • As $x \to +\infty$, $f(x) \to +\infty$.

5. Turning Points: A degree-3 polynomial can have at most $\text{Degree} - 1 = 2$ turning points. The exact coordinates of the turning points require finding the critical points (derivative set to zero). However, they are not computed explicitly on this sheet.

Summary of Answers:

1. X-Intercepts: $2, -4, 3$.
2. Y-Intercept: $(0, 24)$.
3. Degree of Polynomial: 3.
4. End Behavior:
   • $x \to -\infty$: $y \to -\infty$.
   • $x \to +\infty$: $y \to +\infty$.
5. Turning Point: Needs further calculation (critical points).

Do you want me to compute the turning points or provide a detailed graph explanation?

Additional Related Questions:

1. What is the expanded form of $f(x) = (x - 2)(x + 4)(x - 3)$?
2. How do you find the critical points of a cubic function?
3. How can you use the end behavior to sketch the graph of this function?
4. Why does a cubic polynomial have at most two turning points?
5. How do you determine the leading coefficient of a polynomial in factored form?

Tip: When finding turning points, always compute the first derivative $f'(x)$ and solve $f'(x) = 0$ to locate the critical points.