(a) The graph of $y = \left(x+3\right)^{2}+10$ is the graph of $y = x^{2}+10$

shifted horizontally		choose the shifting amount left 5 units left 4 units left 3 units left 2 units left 1 unit no horizontal shift right 1 unit right 2 units right 3 units right 4 units right 5 units and
shifted vertically		choose the shifting amount down 5 units down 4 units down 3 units down 2 units down 1 unit no vertical shift up 1 unit up 2 units up 3 units up 4 units up 5 units .

(b) The graph of $y = x^{2}+11$ is the graph of $y = x^{2}+10$

shifted horizontally		choose the shifting amount left 5 units left 4 units left 3 units left 2 units left 1 unit no horizontal shift right 1 unit right 2 units right 3 units right 4 units right 5 units and
shifted vertically		choose the shifting amount down 5 units down 4 units down 3 units down 2 units down 1 unit no vertical shift up 1 unit up 2 units up 3 units up 4 units up 5 units .

(c) The graph of $y = \left(x+3\right)^{3}-5\!\left(x+3\right)+5$ is the graph of $y = x^{3}-5x$

shifted horizontally		choose the shifting amount left 5 units left 4 units left 3 units left 2 units left 1 unit no horizontal shift right 1 unit right 2 units right 3 units right 4 units right 5 units and
shifted vertically		choose the shifting amount down 5 units down 4 units down 3 units down 2 units down 1 unit no vertical shift up 1 unit up 2 units up 3 units up 4 units up 5 units .

(d) The graph of $y = 3\!\left(x-2\right)^{2}-\left(x-2\right)+9$ is the graph of $y = 3x^{2}-x+10$

shifted horizontally		choose the shifting amount left 5 units left 4 units left 3 units left 2 units left 1 unit no horizontal shift right 1 unit right 2 units right 3 units right 4 units right 5 units and
shifted vertically		choose the shifting amount down 5 units down 4 units down 3 units down 2 units down 1 unit no vertical shift up 1 unit up 2 units up 3 units up 4 units up 5 units .