the vertex of the parabola represented by f(x)=x^2-2x+6 has coordinates (1,5). Find the coordinates of the vertex of the parabol

a defined by g(x)=f(x+3). Explain how you arrived at your answer

Mathematics

1 answer:

Sever21 [200]2 years ago

5 0

$Plug \ in \ x+3 \ into \ f(x) \ to \ get \ g(x)
\\\ g(x) = (x+3)^2-2(x+3)+6
\\\ g(x)= x^2+6x+9 -2x-6+6
\\\ g(x) = x^2+4x+9
\\\ -\frac{b}{2a} --\ \textgreater \ vertex
\\\ \frac {-4}{2}
\\\ x \ coordinate = -2, plug \ it \ back \ into \ g(x)
\\\ (-2)^2+4(-2)+9
\\\ 4-8 + 9
\\\ y \ coordinate = 5
\\\ \boxed{(-2,5)}$

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