To rewrite the given quadratic expression $x^2 + 2x + 4$ in the form $(x + a)^2 + b$ where $a$ and $b$ are integers, we will complete the square.

Step-by-step Solution:

1. Start with the quadratic expression: $x^2 + 2x + 4$

2. Focus on the first two terms ($x^2 + 2x$) and complete the square: Add and subtract $\left(\frac{2}{2}\right)^2 = 1$ inside the expression: $x^2 + 2x + 1 - 1 + 4$

3. Group the perfect square trinomial: $(x^2 + 2x + 1) + (4 - 1)$

4. Rewrite the trinomial as a square: $(x + 1)^2 + 3$

Final Answer:

$x^2 + 2x + 4 = (x + 1)^2 + 3$ Here, $a = 1$ and $b = 3$.

Would you like a detailed explanation of any step? Let me know! 😊

Related Questions:

1. How can completing the square help solve quadratic equations?
2. What is the vertex form of a quadratic equation, and how does it relate to completing the square?
3. Why do we subtract and add the same number when completing the square?
4. Can the method of completing the square be used for non-integer coefficients?
5. What is the geometric interpretation of completing the square?

Tip:

Always double-check your arithmetic when completing the square to avoid small mistakes!