Using the completing-the-square method, rewrite f (x) = x^2-6x+2 in vertex form.

- f (x) = (x-3) ^2

- f (x) = (x-3) ^2 + 2

- f (x) = (x-3) ^2 - 7

- f (x) = (x-3) ^2 + 9

The vertex form of f (x) is f (x) = (x - 3) ² - 7 ⇒ 3rd answer

Step-by-step explanation:

To make a bracket of power two from a quadratic expression do that

Take the term of x and divide its coefficient by 2 Square the quotient Add and subtract this square to the quadratic expression Simplify it and write it in the form (x - h) ² + k

∵ f (x) = x² - 6x + 2

∵ x² = (x) (x)

∴ The first term in the bracket of power 2 is x

- Divide - 6x by 2

∵ - 6x : 2 = - 3x

∴ The second term in the bracket of power 2 is - 3

- Square (-3)

∵ (-3) ² = 9

- Add and subtract 9 to f (x)

∴ f (x) = x² - 6x + 9 - 9 + 2

∴ f (x) = (x² - 6x + 9) - 9 + 2

- Write (x² - 6x + 9) in the form (x - 3) ²

∴ f (x) = (x - 3) ² - 9 + 2

- Add the like terms in the right hand side

∴ f (x) = (x - 3) ² - 7

∴ The vertex form of f (x) is f (x) = (x - 3) ² - 7