https://file.aiquickdraw.com/mathbot/file/1727053652855x9ixsf5z.jpg

To solve this problem, we need to complete the square for the given quadratic equation \( y = x^2 + 6x + 11 \).

### Steps to complete the square:
1. **Start with the quadratic expression** \( x^2 + 6x + 11 \).
2. **Focus on the quadratic and linear terms**: \( x^2 + 6x \). To complete the square, take half of the coefficient of \( x \) (which is 6), square it, and add and subtract this value.
   - Half of 6 is 3.
   - \( 3^2 = 9 \).
   - Now rewrite the equation by adding and subtracting 9:  
   \[
   x^2 + 6x + 9 - 9 + 11 = (x + 3)^2 - 9 + 11
   \]
3. **Simplify the constant terms**:  
   \[
   (x + 3)^2 + 2
   \]
4. The completed square form is:  
   \[
   y = (x + 3)^2 + 2
   \]

The correct answer is **y = (x + 3)^2 + 2**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve a quadratic equation by completing the square?
2. What is the vertex form of a quadratic equation?
3. Can you always complete the square for any quadratic equation?
4. How does completing the square help in graphing parabolas?
5. What is the geometric interpretation of completing the square?

**Tip:** Completing the square is especially useful when converting a quadratic equation into vertex form, which makes identifying the vertex of a parabola easier.

Complete the square to find the equation of the parabola in the problem y = x^2 + 6x + 11.

Learn how to complete the square for the quadratic equation y = x^2 + 6x + 11. This solution transforms the equation into vertex form, which makes it easier to analyze and graph. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation