Question

In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).

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

Short answer

The required graph is

Step-by-step solution

Step 1. Given information.

The given quadratic function is$f\left(x\right)={\left(x-2\right)}^2+2$

Step 2. Determine the horizontal and vertical shift.

Compare the function with$f\left(x\right)={\left(x-h\right)}^2+k$and determine $h\mathrm{and}k$.

localid="1646225284855" $$\begin{gathered} f\left(x\right)={\left(x-2\right)}^2+2 \\ f\left(x\right)=a{\left(x-h\right)}^2+k \\ So,h=2 \\ k=2 \\ a=1 \end{gathered}$$

Step 3. plot the graph  of the parent function.

Plot the graph of $f\left(x\right)=x^2$

Step 4. horizontal shift of the graph 

Shift the graph of $f\left(x\right)=x^2$to 2 units right to plot $f\left(x\right)={\left(x-2\right)}^2$.

Step 5. vertical shift of the graph.

Shift the graph of $f\left(x\right)={\left(x-2\right)}^2$to 2 units up to plot $f\left(x\right)={\left(x-2\right)}^2+2$.