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Chapter 10: Q 67. (page 655)

Graph each function.

f(x)=-64-16x2

Short Answer

Expert verified

The graph of the function is half an ellipse.

Step by step solution

01

Step 1. Given information.

WE have given function is y=-64-16x2.

Now, find an equation of conic, we have

y2=64-16x2y2+16x2=64y264+x24=1x222+y282=1

02

Step 2. Graph of the function.  

We have b=2,a=8in b2=a2-c2

c2=82-22c2=60c=60c=215

The foci are at (0,卤215).

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

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

The graph of the function is

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