Question: User: f(x)=2$x^2$ +5x then find f(x+2)
1. **State the problem:** We are given the function $f(x) = 2x^2 + 5x$ and need to find $f(x+2)$.
2. **Recall the formula:** To find $f(x+2)$, substitute $x+2$ wherever $x$ appears in the function.
3. **Substitute:**
$$f(x+2) = 2(x+2)^2 + 5(x+2)$$
4. **Expand the square:**
$$(x+2)^2 = x^2 + 2\cdot x \cdot 2 + 2^2 = x^2 + 4x + 4$$
5. **Rewrite the expression:**
$$f(x+2) = 2(x^2 + 4x + 4) + 5(x+2)$$
6. **Distribute the constants:**
$$= 2x^2 + 8x + 8 + 5x + 10$$
7. **Combine like terms:**
$$= 2x^2 + (8x + 5x) + (8 + 10) = 2x^2 + 13x + 18$$
**Final answer:**
$$f(x+2) = 2x^2 + 13x + 18$$