Question

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

Answer 1

`x^2+4x-1= \\ x^2+4x+4-4-1= \\ (x+2)^2-4-1= \\ (x+2)^2-5 \\ \\ \boxed{f(x)=(x+2)^2-5}`

Answer 2

f(x) = (x + 2)² - 5

Step-by-step 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