Respuesta :

Answer:

[tex]3(x-1)^2 +6[/tex]

Step-by-step explanation:

Write [tex]3x^2-6x+9[/tex] in the form: [tex]x^2 + 2ax + a^2[/tex].

Factor out 3.

[tex]3(x^2 -2x+3)[/tex]

Add and subtract [tex]\left(-1\right)^2\:[/tex].

[tex]3\left(x^2-2x+3+\left(-1\right)^2-\left(-1\right)^2\right)[/tex]

You dont have to write this section down but its for notes:

[tex]x^2+2ax+a^2=\left(x+a\right)^2[/tex]

[tex]x^2-2x+\left(-1\right)^2=\left(x-1\right)^2[/tex]

Continue writing this down to show work:

Complete the square

[tex]3\left(\left(x-1\right)^2+3-\left(-1\right)^2\right)[/tex]

Simplify

[tex]3\left(x-1\right)^2+6[/tex]

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