Answer:
[tex]f(x) = 3(x - 1)^2-3[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 3x^2 - 6x + 6[/tex]
Required
Write as:
[tex]f(x) = a(x - h)^2 + k[/tex]
In [tex]f(x) = 3x^2 - 6x + 6[/tex], the coefficient of x is -6
Divide by 2: -3
Square: 9
Add 9 - 9 to the above equation
[tex]f(x) = 3x^2 - 6x +9-9+ 6[/tex]
Split to 2
[tex]f(x) = [3x^2 - 6x +9]-[9- 6][/tex]
[tex]f(x) = [3x^2 - 6x +9]-[3][/tex]
Factorize:
[tex]f(x) = [3x^2 - 3x -3x+9]-[3][/tex]
[tex]f(x) = [3x(x - 1) -3(x-1)]-[3][/tex]
[tex]f(x) = [(3x - 3)(x-1)]-[3][/tex]
Factorize 3x - 3
[tex]f(x) = [3(x - 1)(x-1)]-[3][/tex]
[tex]f(x) = 3(x - 1)^2-[3][/tex]
[tex]f(x) = 3(x - 1)^2-3[/tex]
