Function Substitution 33A734

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:** $$(x+2)^2 = x^2 + 4x + 4$$. 5. **Rewrite:** $$f(x+2) = 2(x^2 + 4x + 4) + 5(x+2)$$. 6. **Distribute:** $$= 2x^2 + 8x + 8 + 5x + 10$$. 7. **Combine like terms:** $$= 2x^2 + (8x + 5x) + (8 + 10) = 2x^2 + 13x + 18$$. **Final answer:** $$f(x+2) = 2x^2 + 13x + 18$$.