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.