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The problem asks to evaluate the function \( f(x) = 4x^2 - 5x \) for different values of \( x \).

Let's solve each part:

\[
f(x) = 4x^2 - 5x
\]

1. **(a) \( f(-3) \):**

   \[
   f(-3) = 4(-3)^2 - 5(-3) = 4(9) + 15 = 36 + 15 = 51
   \]

2. **(b) \( f(-2) \):**

   \[
   f(-2) = 4(-2)^2 - 5(-2) = 4(4) + 10 = 16 + 10 = 26
   \]

3. **(c) \( f(-1) \):**

   \[
   f(-1) = 4(-1)^2 - 5(-1) = 4(1) + 5 = 4 + 5 = 9
   \]

4. **(d) \( f(0) \):**

   \[
   f(0) = 4(0)^2 - 5(0) = 0
   \]

5. **(e) \( f(1) \):**

   \[
   f(1) = 4(1)^2 - 5(1) = 4(1) - 5 = 4 - 5 = -1
   \]

### Final answers:
- (a) \( f(-3) = 51 \)
- (b) \( f(-2) = 26 \)
- (c) \( f(-1) = 9 \)
- (d) \( f(0) = 0 \)
- (e) \( f(1) = -1 \)

Would you like more details on any step? 

Here are 5 follow-up questions related to this topic:
1. How would the function change if the coefficient of \( x^2 \) was altered?
2. What is the significance of evaluating a quadratic function at different points?
3. How does the vertex of a quadratic function affect its values?
4. Can you graph this function based on these values?
5. How does factoring the quadratic expression help in finding its roots?

**Tip:** The symmetry of quadratic functions can be used to quickly estimate values near the vertex.

Evaluate the function f(x) = 4x^2 - 5x for the given values of x: (a) f(-3), (b) f(-2), (c) f(-1), (d) f(0), (e) f(1).

This problem involves evaluating the quadratic function f(x) = 4x^2 - 5x at specific values of x. The solution walks through each calculation for values such as f(-3), f(-2), f(-1), f(0), and f(1). Suitable for students in Grades 9-10.

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