Question

determine whether the graph of the equation is symmetric with respect to the y - axis, the x - axis, the origin, more than one of these, or none of these. x = y^{2}+10. select all that apply. x - axis y - axis origin none of these

Explanation:

Step1: Test for x - axis symmetry

Replace \(y\) with \(-y\) in the equation \(x = y^{2}+10\). We get \(x=(-y)^{2}+10\), which simplifies to \(x = y^{2}+10\), the original equation. So, it is symmetric about the x - axis.

Step2: Test for y - axis symmetry

Replace \(x\) with \(-x\) in the equation \(x = y^{2}+10\). We get \(-x=y^{2}+10\), or \(x=-y^{2} - 10\), which is not the original equation. So, it is not symmetric about the y - axis.

Step3: Test for origin symmetry

Replace \(x\) with \(-x\) and \(y\) with \(-y\) in the equation \(x = y^{2}+10\). We get \(-x=(-y)^{2}+10\), or \(-x = y^{2}+10\), or \(x=-y^{2}-10\), which is not the original equation. So, it is not symmetric about the origin.

Answer:

x - axis