Question

The graph of f and g are given. Find a formula for the functiong.

Short answer

$g\left(x\right)={(x-2)}^2$

Step-by-step solution

Step 1. Concept of horizontal shift.

To graph $y=f(x-c)$, shifts the graph $y=f\left(x\right)$ to the right c units

And, to graph$y=f(x+c)$ shifts the graph$y=f\left(x\right)$ to the left c units

Step 2. Given condition.

Given equation is

$f\left(x\right)=x^2$; And the graph of $g\left(x\right)$is

Step 3. Determining the formula for the function g.

The graph shifts right by the 2 units,

So, $$\begin{gathered} c=2 \\ g\left(x\right)={\left(x-2\right)}^2 \end{gathered}$$