Question

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

Answer 1

Answer:

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