Respuesta :
Answer:
(-1,-6)
Step-by-step explanation:
[tex]f(x)=x^2+6x+3[/tex]
[tex]g(x)=f(x-2)[/tex]
[tex]g(x)=(x-2)^2+6(x-2)+3[/tex] (Replaced x in f with (x-2))
[tex]g(x)=x^2-4x+4+6x-12+3[/tex] (Used [tex](x+b)^2=x^2+2bx+b^2[/tex] and distributive property)
[tex]g(x)=x^2-4x+6x+4-12+3[/tex] (Gathered like terms)
[tex]g(x)=x^2+2x-5[/tex] (Simplified)
The vertex of a parabola occurs at [tex](\frac{-b}{2a},g(\frac{-b}{2a})[/tex].
Let's find [tex]\frac{-b}{2a}[/tex] first.
[tex]\frac{-2}{2(1)}=-1[/tex]
Now we can obtain [tex]g(\frac{-b}{2a})[/tex] which is [tex]g(-1)[/tex] in this case:
[tex]g(x)=x^2+2x-5[/tex]
[tex]g(-1)=(-1)^2+2(-1)-5[/tex]
[tex]g(-1)=1-2-5[/tex]
[tex]g(-1)=-1-5[/tex]
[tex]g(-1)=-6[/tex].
The vertex is (-1,-6).
Answer:
(-5,-6)
Step-by-step explanation:
just took the test and got it right
