# To graph: The equation y = 16 − x 2 and check the equation for symmetry.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 115RE
To determine

## To graph: The equation y=16−x2 and check the equation for symmetry.

Expert Solution

The equation y=16x2 is symmetric about y -axis but not about x -axis and the graph is as follows:

### Explanation of Solution

Given information:

The equation of line y=16x2

Formula used:

The equation is said to have symmetry about the x -axis when the equation remains unchanged on replacing y by y

Graphically it can be said that the graph remains unchanged when reflected in the x -axis.

The equation is said to have symmetry about the y -axis when the equation remains unchanged on replacing x by x

Graphically it can be said that the graph remains unchanged when reflected in the y -axis.

The equation is said to have symmetry about the origin if it is symmetric about x -axis and y -axis that is the equation remains unchanged on replacing x by x or y by y

Graphically it can be said that the graph remains unchanged when rotated with an angle of 180 about the origin.

Calculation:

It is provided that the equation of line is y=16x2  (1)

Firstly replace y by y in (1)

y=16x2y=16+x2

The equation obtained is not the same as the original one.

Hence, y=16x2 is not symmetric about x -axis

Next, replace x by x in (1)

y=16(x)2y=16x2

The equation obtained is the same as the original one.

Hence, y=16x2 is symmetric about y -axis.

For plotting:

 x y=16−x2 (x.y) 02−2 161212 (0,16)(2,12)(−2,12)

We plot these points to get the graph as follows:

Thus, y=16x2 is symmetric about y -axis but not about x -axis.

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