The problem asks to evaluate $f(k - 3)$ given that $f(x) = x^2 - 2x$.

Solution:

We start by substituting $k - 3$ into the function $f(x)$.

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

Step 1: Expand $(k - 3)^2$:

$(k - 3)^2 = k^2 - 6k + 9$

Step 2: Expand $-2(k - 3)$:

$-2(k - 3) = -2k + 6$

Step 3: Combine terms:

$f(k - 3) = k^2 - 6k + 9 - 2k + 6$

$f(k - 3) = k^2 - 8k + 15$

So, the final answer is:

$f(k - 3) = k^2 - 8k + 15$

Would you like further explanation or a deeper breakdown?

Here are 5 related questions to extend your understanding:

1. What is the general formula for evaluating $f(a + b)$ for any function $f(x)$?
2. How do you solve $f(x) = 0$ for this function?
3. If $f(x) = x^2 - 2x$, what is the vertex of the parabola?
4. How do you determine whether this function is increasing or decreasing for different values of $x$?
5. How would the answer change if the function was $f(x) = x^2 + 2x$ instead?

Tip: When substituting a term into a function, always expand carefully and combine like terms to avoid mistakes!