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 ：\(\boxed{g(x)=(x-7)^{2}+3}\)