Question

Complete the square to find the value of k in the parabola in the problem y=x²+6x+11.

Answer 1

To complete the square for the given parabola equation, y = x² + 6x + 11, we follow the steps of grouping the terms, adding the square term, simplifying and factoring, and isolating the square term. The value of k in the parabola equation y = x² + 6x + 11 is 2.

Step-by-step explanation:

To complete the square for the given parabola equation, y = x² + 6x + 11, we follow these steps:

1. Group the terms containing x² and x together: y = (x² + 6x) + 11
2. Take half of the coefficient of x, square it, and add it to both sides of the equation: y + (3²) = (x² + 6x + (3²)) + 11
3. Simplify and factor the trinomial inside the parentheses: y + 9 = (x + 3)² + 11
4. Subtract 9 from both sides to isolate the square term: y = (x + 3)² + 2

Therefore, the value of k in the parabola equation y = x² + 6x + 11 is 2.