Answer:
[tex]f(x)=(x-3)^2-7[/tex]
Step-by-step explanation:
Use the formula:
[tex]x^2+bx+c \implies (x+\frac{b}{2})^2-(\frac{b}{2}{)^2+c[/tex]
[tex]f(x) = x^2 - 6x + 2[/tex]
[tex]\implies f(x)=(x-\frac62)^2-(\frac62)^2+2[/tex]
[tex]\implies f(x)=(x-3)^2-3^2+2[/tex]
[tex]\implies f(x)=(x-3)^2-9+2[/tex]
[tex]\implies f(x)=(x-3)^2-7[/tex]
[tex]\\ \rm\hookrightarrow x^2-6x+2[/tex]
[tex]\\ \rm\hookrightarrow x^2-2(3)(x)+2[/tex]
[tex]\\ \rm\hookrightarrow x^2-2(3x)+3^2-3^2+2[/tex]
[tex]\\ \rm\hookrightarrow (x-3)^2-9+2[/tex]
[tex]\\ \rm\hookrightarrow (x-3)^2-7[/tex]
