Chapter 3 - Quadratic Functions - 3.2 The Vertex of a Parabola - Exercises and Problems for Section 3.2 - Exercises and Problems - Page 128: 42

a) $g(x)=f(x-3)+2$ b) Yes. c) See the graph

a) The graph of $g$ can be found by shifting the graph of $f$ to the right 3 units and then up 2 units; $g(x)=f(x-3)+2$. b) Yes, $g$ is a quadratic function. Since $$ \begin{aligned} g(x) & =(x-3)^2+2 \\ & =x^2-6 x+11 \end{aligned} $$ c) See the graph