Chapter 1: Functions - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises 1.2 - Page 19: 22

(a) $y=x^2+3$ (b) $y=x^2-5$

The graph in Position $(a)$ is the graph of $y=x^2$ shifted up 3 units. Hence, the equation for this graph is $y=x^2+3.$ Similarly, the graph in Position $(b)$ is the graph of $y=x^2$ shifted down 5 units. Hence, the equation for this graph is $y=x^2-5.$