Which of the following equations represents the quadratic relation y = x2 + 4x + 6 in the form y = a(x − h)2 + k?

The equation y = x^2 + 4x + 6 can be rewritten in the form y = a(x - h)^2 + k by completing the square. Here are the steps:

1. First, we rewrite the equation y = x^2 + 4x + 6 in the form y = x^2 + 4x + __ + 6 - __. We want to find a number that completes the square in the first three terms.

2. The number that completes the square is (b/2)^2, where b is the coefficient of x. In this case, b is 4, so (b/2)^2 = (4/2)^2 = 2^2 = 4.

3. We insert this number into the blanks in our equation from step 1, giving us y = x^2 + 4x + 4 + 6 - 4.

4. Simplifying this gives us y = (x^2 + 4x + 4) + 2.

5. The expression in the parentheses is a perfect square, which we can write as (x + 2)^2. This gives us y = (x + 2)^2 + 2.

So, the equation y = x^2 + 4x + 6 in the form y = a(x - h)^2 + k is y = (x + 2)^2 + 2, where a = 1, h = -2, and k = 2.