171k views
0 votes
PLEASE QUICK!!!

Complete this activity. Include all of your work in your final answer. Submit your solution.

Given: f(x) = x^2 + 2x + 1, find f(x + h) and simplify.

2 Answers

2 votes

Explanation:

To find f(x + h), we substitute x + h for x in the function f(x):

f(x + h) = (x + h)^2 + 2(x + h) + 1

Now we simplify by expanding the square:

f(x + h) = x^2 + 2hx + h^2 + 2x + 2h + 1

We can combine like terms to simplify this expression:

f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1)

Therefore, f(x + h) = x^2 + (2h + 2)x + (h^2 + 2h + 1).

User Florian Pfisterer
by
8.7k points
2 votes

Answer:


f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1

Explanation:

In this question, we have to plug (x + h) into the given function and simplify.


f(x) = x^2 + 2x + 1

replacing all instances of x with (x + h)


f(x+h) = (x+h)^2 + 2(x+h) + 1

expanding the quadratic term (x + h)²


f(x+h) = (x^2 + 2xh + h^2) + 2(x+h) + 1

↓ applying the distributive property ...
2(x+h) = 2x + 2h


\boxed{f(x+h) = x^2 + 2xh + h^2 + 2x+2h + 1}

No further simplification can be done.

User Bart Burg
by
8.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.