Question

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

Answer 1

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