To solve for \( f(2x - 3) \) given the function \( f(x) = x^2 - 2x + 2 \), we'll substitute \( 2x - 3 \) in place of \( x \) in the function.

1. Start with the original function:
   \[
   f(x) = x^2 - 2x + 2
   \]

2. Substitute \( 2x - 3 \) for \( x \):
   \[
   f(2x - 3) = (2x - 3)^2 - 2(2x - 3) + 2
   \]

3. Expand and simplify:
   \[
   (2x - 3)^2 = (2x - 3)(2x - 3) = 4x^2 - 12x + 9
   \]
   \[
   -2(2x - 3) = -4x + 6
   \]

4. Combine all the terms:
   \[
   f(2x - 3) = 4x^2 - 12x + 9 - 4x + 6 + 2
   \]
   \[
   f(2x - 3) = 4x^2 - 16x + 17
   \]

So, \( f(2x - 3) = 4x^2 - 16x + 17 \).

Would you like to explore further details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. What is the derivative of the function \( f(x) = 4x^2 - 16x + 17 \)?
2. How would you find the vertex of the parabola represented by \( f(2x - 3) \)?
3. How do you determine if the function \( f(x) = 4x^2 - 16x + 17 \) has any real roots?
4. Can you find the y-intercept of the function \( f(2x - 3) \)?
5. How does the transformation of \( f(x) = x^2 - 2x + 2 \) to \( f(2x - 3) \) affect its graph?

**Tip:** When substituting expressions into functions, always remember to fully expand and simplify the terms to avoid errors in calculations.

Learn how to calculate f(2x - 3) using the function f(x) = x^2 - 2x + 2. Follow a step-by-step solution with detailed algebraic calculations and substitutions. Suitable for high school students studying algebra and quadratic equations.

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