The problem asks for the result of $f(-x)$ for the given function $f(x) = 2x^2 + 3x - 4$.

To solve this:

1. Start with the function:
   $f(x) = 2x^2 + 3x - 4$

2. Substitute $-x$ for $x$ in the function:
   $f(-x) = 2(-x)^2 + 3(-x) - 4$

3. Simplify each term:

   • $(-x)^2 = x^2$, so $2(-x)^2 = 2x^2$
   • $3(-x) = -3x$
   • The constant term, $-4$, remains the same.

Thus, $f(-x) = 2x^2 - 3x - 4$.

The correct answer is a. $2x^2 - 3x - 4$.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you determine whether a function is even, odd, or neither?
2. What is the significance of substituting $-x$ into a function?
3. How do different powers of $x$ affect the behavior of $f(-x)$?
4. Can you graph the function $f(x) = 2x^2 + 3x - 4$ and its reflection $f(-x)$?
5. How would the answer change if the function had a different form, like $f(x) = x^3 + x$?

Tip: A function is even if $f(-x) = f(x)$ for all $x$, and odd if $f(-x) = -f(x)$.