You are given the function \( f(x+h) = 2(x+h)^2 + 3(x+h) - 1 \). To simplify this expression, we'll expand and combine like terms.

### Step 1: Expand the squared term
\[
(x+h)^2 = x^2 + 2xh + h^2
\]

### Step 2: Substitute into the function
\[
f(x+h) = 2(x^2 + 2xh + h^2) + 3(x+h) - 1
\]

### Step 3: Distribute the constants
\[
f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1
\]

### Step 4: Combine like terms
\[
f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1
\]

So, the expanded form of \( f(x+h) \) is:
\[
f(x+h) = 2x^2 + 4xh + 2h^2 + 3x + 3h - 1
\]

Would you like further details or have any questions on this? Here are five questions to expand the topic:

1. How does the function \( f(x) = 2x^2 + 3x - 1 \) look when you substitute specific values of \( h \)?
2. What happens when you calculate the derivative of \( f(x) \)?
3. How do you find the limit of \( f(x+h) \) as \( h \) approaches 0?
4. What is the significance of the terms \( 4xh \) and \( 2h^2 \) in this context?
5. How would this process change if the original function

Discover how to expand and simplify the function f(x+h) = 2(x+h)^2 + 3(x+h) - 1 step by step. This algebraic problem covers polynomial expansion and distribution concepts, suitable for students in Grades 9-11.

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