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

Answer

f(x) = (x + 2)² - 5

Explanation

f(x) = x² + 4x − 1

Let y = f(x)

y = x² + 4x − 1

y + 1 = x² + 4x

Make the right hand of the equation a perfect square by adding (b/2)² on both sides.

y + 1 + (4/2)² = x² + 4x + (4/2)²

y + 1 + 4 = x² + 4x + 2²

y + 5 = (x + 2)²

Subtracting 5 on both sides.

y + 5 - 5 = (x + 2)² - 5

y = (x + 2)² - 5

Now replace y with f(x)

f(x) = (x + 2)² - 5

expression #3 is not equivalent. the others are.