Problem

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 $g(x)$.

Solution

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

From Solvely APP
Source: https://solvelyapp.com/problems/8404/

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