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Chapter 10: Q 65. (page 655)

Graph each function.

f(x)=16-4x2.

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 y=16-4x2

Now, find equation of conic in a standard form we have

role="math" localid="1646757247233" y2=(16-4x2)2y2=16-4x2y2+4x2=16y216+4x216=1616y216+x24=1x222+y242=1

02

Step 2. Graph of the function.

Substitute b=2and a=4inb2=a2-c2.

c2=42-22c2=12c=12c=23

The foci at (0,卤23).

The vertices of the major axis of the ellipse are at (0,4)and (0,-4).

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

Use the vertices and foci of the ellipse to graph the function is

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