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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?

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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!

Learn how to evaluate f(k - 3) for the quadratic function f(x) = x² - 2x by using algebraic substitution and expanding binomials. This step-by-step guide walks through the process of expanding (k - 3)² and simplifying the expression, suitable for students in Grades 9-10.

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