To find \( g(x+5) \) when \( g(x) = x^2 - 2x \), follow these steps:

1. **Substitute \( x+5 \) into the function \( g(x) \):**
   \[
   g(x+5) = (x+5)^2 - 2(x+5)
   \]

2. **Expand the squared term:**
   \[
   (x+5)^2 = x^2 + 10x + 25
   \]
   So,
   \[
   g(x+5) = x^2 + 10x + 25 - 2(x+5)
   \]

3. **Distribute and simplify:**
   \[
   g(x+5) = x^2 + 10x + 25 - 2x - 10
   \]

4. **Combine like terms:**
   \[
   g(x+5) = x^2 + 8x + 15
   \]

So, \( g(x+5) = x^2 + 8x + 15 \).

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What is \( g(x-3) \) if \( g(x) = x^2 - 2x \)?
2. How do you find the vertex of the quadratic function \( g(x) = x^2 - 2x \)?
3. How does shifting the graph horizontally affect the equation of \( g(x) \)?
4. What is the axis of symmetry for the function \( g(x) = x^2 - 2x \)?
5. Can you factorize \( g(x) = x^2 - 2x \)?

**Tip:** When dealing with functions, substituting values (like \( x+5 \)) can shift the graph horizontally.

Learn how to find g(x+5) for the function g(x) = x^2 - 2x. Follow a step-by-step solution including function substitution, polynomial expansion, and simplification. Suitable for high school students and those interested in quadratic equations.

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