Question

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

Answer 1

f(x) = x² + 4x - 1
y = x² + 4x - 1
y + 1 = x² + 4x - 1 + 1
y + 1 = x² + 4x
y + 1 + 4 = x² + 4x + 4
y + 5 = x² + 2x + 2x + 4
y + 5 = x(x) + x(2) + 2(x) + 2(2)
y + 5 = x(x + 2) + 2(x + 2)
y + 5 = (x + 2)(x + 2)
y + 5 = (x + 2)²
y + 5 - 5 = (x + 2)² - 5
y = (x + 2)² - 5
f(x) = (x + 2)² - 5