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Q 67.

Expert-verified
Found in: Page 655

### Precalculus Enhanced with Graphing Utilities

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

# Graph each function. $f\left(x\right)=-\sqrt{64-16{x}^{2}}$

The graph of the function is half an ellipse.

See the step by step solution

## Step 1. Given information.

WE have given function is $y=-\sqrt{64-16{x}^{2}}$.

Now, find an equation of conic, we have

${y}^{2}=64-16{x}^{2}\phantom{\rule{0ex}{0ex}}{y}^{2}+16{x}^{2}=64\phantom{\rule{0ex}{0ex}}\frac{{y}^{2}}{64}+\frac{{x}^{2}}{4}=1\phantom{\rule{0ex}{0ex}}\frac{{x}^{2}}{{2}^{2}}+\frac{{y}^{2}}{{8}^{2}}=1$

## Step 2. Graph of the function.

We have $b=2,a=8$ in ${b}^{2}={a}^{2}-{c}^{2}$

${c}^{2}={8}^{2}-{2}^{2}\phantom{\rule{0ex}{0ex}}{c}^{2}=60\phantom{\rule{0ex}{0ex}}c=\sqrt{60}\phantom{\rule{0ex}{0ex}}c=2\sqrt{15}$

The foci are at $\left(0,±2\sqrt{15}\right)$.

The vertices of the major axis of the ellipse are at $\left(0,8\right)$and $\left(0,-8\right)$.

The vertices of the minor axis of the ellipse are at $\left(2,0\right)$ and $\left(-2,0\right)$.

The graph of the function is