The function $g(x)$ is obtained by translating $f(x)=x^2$ to the right 7 units and up 3 units. Write an equation for $g(x)$.

Step 1 ：The function $f(x)=x^2$ is a simple quadratic function.

Step 2 ：When we translate it to the right by 7 units, we replace $x$ with $(x-7)$ in the equation. This is because when we move the graph to the right, the $x$-values of the points on the graph increase, so we need to subtract 7 from $x$ to get the same $y$-values as before.

Step 3 ：Similarly, when we translate the function up by 3 units, we add 3 to the equation. This is because when we move the graph up, the $y$-values of the points on the graph increase, so we need to add 3 to get the same $y$-values as before.

Step 4 ：Therefore, the equation for $g(x)$ should be $g(x)=(x-7{)}^2+3$.

Step 5 ：$\boxed{{\displaystyle g(x)=(x-7{)}^2+3}}$