To solve \( g(a+3) \) for the given function \( g(x) = x^2 + 4x - 2 \), we substitute \( a+3 \) into the function \( g(x) \) in place of \( x \).

\[
g(a+3) = (a+3)^2 + 4(a+3) - 2
\]

### Step 1: Expand \( (a+3)^2 \)
\[
(a+3)^2 = a^2 + 6a + 9
\]

### Step 2: Expand \( 4(a+3) \)
\[
4(a+3) = 4a + 12
\]

### Step 3: Combine everything
\[
g(a+3) = (a^2 + 6a + 9) + (4a + 12) - 2
\]

### Step 4: Simplify
\[
g(a+3) = a^2 + 6a + 9 + 4a + 12 - 2
\]
\[
g(a+3) = a^2 + 10a + 19
\]

Thus, \( g(a+3) = a^2 + 10a + 19 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the derivative of \( g(x) = x^2 + 4x - 2 \)?
2. What is the value of \( g(2) \) for the given function?
3. How can you find the roots of the quadratic function \( g(x) = x^2 + 4x - 2 \)?
4. What is the vertex of the parabola described by \( g(x) = x^2 + 4x - 2 \)?
5. How does the function \( g(x) = x^2 + 4x - 2 \) shift when you graph \( g(x+3) \)?

**Tip:** When substituting values into functions, always simplify step by step to avoid mistakes in the process.

Learn how to solve g(a+3) for the quadratic function g(x) = x^2 + 4x - 2. This solution involves function substitution, polynomial expansion, and simplifying algebraic expressions. Ideal for students in Grades 8-10.

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