Question

Write the expression x2 - 6x-2 in the form (x + a)² + b

Answer 1

`(x-3)^2-11`

Explanation:

Given quadratic expression:

`x^2-6x-2`

To write the given expression in the form (x + a)² + b, complete the square.

Add and subtract the square of half the coefficient of the term in x:

`\implies x^2-6x+\left((-6)/(2)\right)^2-2-\left((-6)/(2)\right)^2`

Simplify:

`\implies x^2-6x+\left(-3\right)^2-2-\left(-3\right)^2`

`\implies x^2-6x+9-2-9`

The first three terms x² - 6x + 9 form a perfect square trinomial.

A perfect square trinomial can be written as the square of a binomial.

Factor the perfect square trinomial:

`\implies(x-3)^2-2-9`

Simplify:

`\implies(x-3)^2-11`

Therefore, the given expression written in the form (x + a)² + b is:

`\boxed{(x-3)^2-11}`

Answer 2

• (x - 3)² - 11

--------------------------

Given

• Expression x² - 6x - 2.

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

• x² - 6x - 2 =
• x² - 2*3*x + 3² - 3² - 2 =
• (x - 3)² - 9 - 2 =
• (x - 3)² - 11