Q. 6 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

The required graph is 

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 $h \mathrm{and} k$.

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

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