Given the equation:

$f(x) = 2x^2 - 3x$

and $x = -4$, we can find $f(-4)$ by substituting $-4$ for $x$:

1. Substitute $-4$ into the equation: $f(-4) = 2(-4)^2 - 3(-4)$

2. Calculate $(-4)^2$: $(-4)^2 = 16$

3. Substitute $16$ into the equation: $f(-4) = 2 \cdot 16 - 3(-4)$

4. Calculate $2 \cdot 16$: $2 \cdot 16 = 32$

5. Calculate $-3 \cdot (-4)$: $-3 \cdot (-4) = 12$

6. Substitute these values back: $f(-4) = 32 + 12 = 44$

Therefore, the answer is:

$f(-4) = 44$

Would you like more details on any step?

Here are some related questions to deepen your understanding:

1. How would the answer change if $x = 4$ instead of $-4$?
2. What happens to the function $f(x)$ as $x$ increases?
3. How can we rewrite $f(x) = 2x^2 - 3x$ in vertex form?
4. How does the value of $f(x)$ change if we multiply the entire function by a constant?
5. What is the derivative of $f(x) = 2x^2 - 3x$ and what does it represent?

Tip: When substituting negative values into equations, remember to use parentheses to avoid sign errors, especially with exponents.