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(Section 9)

A knowledge of y-axis symmetry, x-axis symmetry, and origin symmetry can assist you in sketching a curve. The following guidelines can be used to determine which type of symmetry an equation possesses.

Guidelines for Determining Symmetry

x-axis symmetry: A graph of an equation is symmetric with respect to the x-axis if a substitution of -y for y leads to an equivalent equation.
graph
y2 -2 = x - 3 
(-y)2 - 2 = x - 3 
or
y2 -2 = x - 3
so this equation has 
x-axis symmetry.
y-axis symmetry: A graph of an equation is symmetric with respect to the y-axis if a substitution of -x for x leads to an equivalent equation.
y = x2 + 4   
y = (-x)2 + 4 = x2 + 4 
or
y = x2 + 4
so this equation has
y-axis symmetry
graph
origin symmetry: A graph of an equation is symmetric respect to the origin of the simultaneous substitution of -x for x and -y for y leads to an equivalent equation.
x2 + y2 = 16
graph
Check Your Understanding: (Remember to write your answers down to these questions.)
  1. Check these questions for symmetry. Support why each has a specific type of symmetry.
equation
equation
equation
  1. Write an equation which has
X-axis symmetry
Y-axis symmetry
Origin symmetry

Table of Contents

Section 8

Answer Section

Section 10

This page was modified on 03/21/16 by

Rahn, 2000