# Find the Symmetry -10x^3+25x+x^5

Write the polynomial as an equation.
There are three types of symmetry:
1. X-Axis Symmetry
2. Y-Axis Symmetry
3. Origin Symmetry
If exists on the graph, then the graph is symmetric about the:
1. X-Axis if exists on the graph
2. Y-Axis if exists on the graph
3. Origin if exists on the graph
Check if the graph is symmetric about the x-axis by plugging in for .
Remove parentheses.
Since the equation is not identical to the original equation, it is not symmetric to the x-axis.
Not symmetric to the x-axis
Check if the graph is symmetric about the y-axis by plugging in for .
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
Apply the product rule to .
Raise to the power of .
Since the equation is not identical to the original equation, it is not symmetric to the y-axis.
Not symmetric to the y-axis
Check if the graph is symmetric about the origin by plugging in for and for .
Solve for .
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
Apply the product rule to .
Raise to the power of .
Remove parentheses.
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
Apply the product rule to .
Raise to the power of .
Multiply .
Multiply by .
Multiply by .
Simplify .
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
Multiply by .
Apply the product rule to .
Raise to the power of .
Apply the distributive property.
Simplify.
Multiply by .
Multiply by .
Multiply .
Multiply by .
Multiply by .
Since the equation is identical to the original equation, it is symmetric to the origin.
Symmetric with respect to the origin
Find the Symmetry -10x^3+25x+x^5