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Q. 7

Expert-verifiedFound in: Page 174

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

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

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

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

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

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

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

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