Using the completing-the-square method, rewrite f(x) = x² + 4x - 1 in vertex form.

Solution:

The vertex form of the equation is given by

f(x) = a(x - h)² + k

Given, f(x) = x² + 4x - 1

Converting to vertex form,

x² - 6x + 2 = x² + 4x + 4 - 4 - 1

f(x) + 4 = (x + 2)² - 1

f(x) = (x + 2)² - 4 - 1

f(x) = (x + 2)² - 5

Therefore, the equation in vertex form is f(x) = (x + 2)² - 5.

Using the completing-the-square method, rewrite f(x) = x² + 4x - 1 in vertex form.

Summary:

Using the completing the square method, the equation f(x) = x² + 4x - 1 in vertex form is f(x) = (x + 2)² - 5.