Question

Write the quadratic function in the form f (x)= a (x - h)' + k.
f (x) = 3x² - 6x+6

Answer 1

`f(x) = 3(x - 1)^2-3`

Explanation:

Given

`f(x) = 3x^2 - 6x + 6`

Required

Write as:

`f(x) = a(x - h)^2 + k`

In
`f(x) = 3x^2 - 6x + 6`, the coefficient of x is -6

Divide by 2: -3

Square: 9

Add 9 - 9 to the above equation

`f(x) = 3x^2 - 6x +9-9+ 6`

Split to 2

`f(x) = [3x^2 - 6x +9]-[9- 6]`

`f(x) = [3x^2 - 6x +9]-[3]`

Factorize:

`f(x) = [3x^2 - 3x -3x+9]-[3]`

`f(x) = [3x(x - 1) -3(x-1)]-[3]`

`f(x) = [(3x - 3)(x-1)]-[3]`

Factorize 3x - 3

`f(x) = [3(x - 1)(x-1)]-[3]`

`f(x) = 3(x - 1)^2-[3]`

`f(x) = 3(x - 1)^2-3`