Given the function $f(x) = x^2 - 3x$, we are asked to evaluate $f(x - 4)$.

Step 1: Substitute $x - 4$ into the function

To find $f(x - 4)$, substitute $x - 4$ for $x$ in the expression for $f(x)$:

$f(x - 4) = (x - 4)^2 - 3(x - 4)$

Step 2: Expand $(x - 4)^2$ and simplify

First, expand the square: $(x - 4)^2 = x^2 - 8x + 16$

Now, distribute the -3 over $(x - 4)$: $-3(x - 4) = -3x + 12$

Step 3: Combine all terms

Now combine the two expressions: $f(x - 4) = (x^2 - 8x + 16) + (-3x + 12)$ Simplify by combining like terms: $f(x - 4) = x^2 - 11x + 28$

Final Answer:

$f(x - 4) = x^2 - 11x + 28$

Do you need further details or explanations?

Here are 5 related questions for practice:

1. What is $f(x + 3)$ for the function $f(x) = x^2 - 3x$?
2. How would you solve $f(2)$ for the same function?
3. How do you find the vertex of the quadratic function $f(x) = x^2 - 11x + 28$?
4. What are the roots of $f(x - 4) = 0$?
5. How would you differentiate $f(x) = x^2 - 3x$?

Tip: When substituting into functions, simplify expressions step by step to avoid errors.