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Q. 7

Expert-verified
Found in: Page 174

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# In Problems 6– 8, graph each quadratic function using transformations (shifting, compressing, stretching, and/or reflecting).$f\left(x\right)=-{\left(x-4\right)}^{2}$

The required graph is

See the step by step solution

## 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 $h\mathrm{and}k$.

localid="1646225245025" $f\left(x\right)=-{\left(x-4\right)}^{2}\phantom{\rule{0ex}{0ex}}f\left(x\right)=a{\left(x-h\right)}^{2}+k\phantom{\rule{0ex}{0ex}}So,h=4\phantom{\rule{0ex}{0ex}}k=0\phantom{\rule{0ex}{0ex}}a=-1$

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