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determine whether the equation has a graph that is symmetric with respect to the​ x-axis, the​ y-axis, the​ origin, or none of these.  y=x2+12

determine whether the equation has a graph that is symmetric with respect to the​ x-axis, the​ y-axis, the​ origin, or none of these.  y=x2+12

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Without​ graphing, determine whether the equation has a graph that is symmetric with respect to the​ x-axis, the​ y-axis, the​ origin, or none of these. 
y=x2+12
Expert Solution
Step 1

Given Data:

Equation: y=x2+12 ......1

 

For symmetric with respect to x-axis,

Substitute -y for y in equation (1).

-y=x2+12y=-x2+12

 

As the obtained equation is not equivalent to equation (1), it is clear that the graph is not symmetric with respect to the x-axis.

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