The standard form of the equation of a parabola is y = x2 + 4x + 11.What is the vertex form of the equation?

The vertex form of a parabola's equation is given by y = a(x-h)² + k, where (h, k) is the vertex of the parabola.

To convert the standard form y = x² + 4x + 11 into vertex form, we need to complete the square for the x terms.

Here are the steps:

1. Group the x terms together: y = (x² + 4x) + 11.

2. To complete the square, we need to add and subtract the square of half the coefficient of x inside the bracket. Half of 4 is 2, and 2² is 4. So, we add and subtract 4 inside the bracket: y = (x² + 4x + 4 - 4) + 11.

3. Simplify the equation: y = (x² + 4x + 4) - 4 + 11.

4. The expression inside the bracket is a perfect square trinomial, which can be written as (x + 2)². So, the equation becomes: y = (x + 2)² - 4 + 11.

5. Simplify the equation to get the vertex form: y = (x + 2)² + 7.

So, the vertex form of the equation y = x² + 4x + 11 is y = (x + 2)² + 7.