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

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Sam Henry

Mathematics

13 October, 19:23

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

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Hammer · 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