Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

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

$f\left(x\right)=-{\left(x-4\right)}^2$

Step-by-Step Solution

Answer

The required graph is 

Step 1. Given information.

The given quadratic function is  $f\left(x\right)=-{\left(x-4\right)}^2$

Step 2. Determine the horizontal and vertical shift.

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

$$\begin{gathered} f\left(x\right)=-{\left(x-4\right)}^2 \\ f\left(x\right)=a{\left(x-h\right)}^2+k \\ So, h=4 \\ k=0 \\ a=-1 \end{gathered}$$

Step 3. plot the graph of the parent function.

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

Step 4. Reflect the graph about x-axis.

Reflect the graph of $f\left(x\right)=x^2$about x-axis to plot $f\left(x\right)=-x^2$.

Step 5. Horizontal shift of the graph.

Shift the graph of $f\left(x\right)=-x^2$ to 4 units right to plot $f\left(x\right)=-{(x-4)}^2$.