I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 4.7 : Symmetry
3. Determine the symmetry of each of the following equation.
\[{x^2} = 7y - {x^3} + 2\]Show All Steps Hide All Steps
Start SolutionLet’s first check for symmetry about the \(x\)-axis. To do this we need to replace all the \(y\)’s with –\(y\).
\[{x^2} = 7\left( { - y} \right) - {x^3} + 2\hspace{0.25in} \to \hspace{0.25in}{x^2} = - 7y - {x^3} + 2\]The resulting equation is not equivalent to the original equation (i.e. it is not same nor is it the same equation except with opposite signs on every term). Therefore, the equation is does not have symmetry about the \(x\)-axis.
Show Step 2Next, we’ll check for symmetry about the \(y\)-axis. To do this we need to replace all the \(x\)’s with –\(x\).
\[{\left( { - x} \right)^2} = 7y - {\left( { - x} \right)^3} + 2\hspace{0.25in} \to \hspace{0.25in}{x^2} = 7y + {x^3} + 2\]The resulting equation is not equivalent to the original equation (i.e. it is not same nor is it the same equation except with opposite signs on every term). Therefore, the equation is does not have symmetry about the \(y\)-axis.
Show Step 3Finally, a check for symmetry about the origin. For this check we need to replace all the \(y\)’s with –\(y\) and to replace all the \(x\)’s with –\(x\).
\[{\left( { - x} \right)^2} = 7\left( { - y} \right) - {\left( { - x} \right)^3} + 2\hspace{0.25in} \to \hspace{0.25in}{x^2} = - 7y + {x^3} + 2\]The resulting equation is not equivalent to the original equation (i.e. it is not same nor is it the same equation except with opposite signs on every term). Therefore, the equation does not have symmetry about the origin.