if X is equal to -4 and the equation is: f(x) = 2x to the second power minus 3x what is the answer

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.

Learn how to evaluate the function f(x) = 2x^2 - 3x when x = -4 with a clear, step-by-step solution. This guide covers core algebraic concepts such as substitution and solving quadratic expressions, making it suitable for students in Grades 7-9.

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