## It looks like you made a couple of mistakes in your calculations. Let's go through it step by step to find the vertex form of the equation.

Starting with the given equation, y = x^2 + 4x - 1:

Step 1: Complete the square for the x^2 and x terms.

To complete the square for the x^2 term, you take half of the coefficient of the x term (4 in this case) and square it. Half of 4 is 2, and 2 squared is 4. So, we add 4 inside the parentheses:

y = (x^2 + 4x + 4) - 4 - 1.

Now we complete the square for the x term:

y = (x^2 + 4x + 4) - 4 - 1.

Step 2: Simplify the equation inside the parentheses.

The expression (x^2 + 4x + 4) can be factored as (x + 2)(x + 2), which is equal to (x + 2)^2.

y = (x + 2)^2 - 4 - 1.

Step 3: Simplify the constants.

The equation now becomes:

y = (x + 2)^2 - 5.

Therefore, the vertex form of the equation y = x^2 + 4x - 1 is y = (x + 2)^2 - 5.

Make sure to double-check your calculations to identify any mistakes.