Find the vertex of the following quadratic function f (x) = x^2+2x+1

The answer is that the vertex is: (1, 0)

Step-by-step explanation:

Use the "Completing the Square Method":

(x - h) ^2 - k = 0, the vertex is (h, - k)

Complete the square:

x^2 + 2x + 1 = 0

x^2 + 2x = - 1

(2/2) ^2 = 1, add 1 to both sides of the equation.

x^2 + 2x + 1 = - 1 + 1

(x + 1) ^2 = 0

(x + 1) ^2 - 0 = 0 (Just to put a placeholder in for he - k)

The vertex is (1, 0)