Determine if the following equation has $x$-axis symmetry, $y$-axis symmetry, origin symmetry, or none of these.
\[
x+y^{2}=1
\]

Step 1 ：Determine if the following equation has x-axis symmetry, y-axis symmetry, origin symmetry, or none of these: \(x+y^{2}=1\)

Step 2 ：To determine the symmetry of the equation, we need to perform the following tests:

Step 3 ：For x-axis symmetry, replace y with -y in the equation. If the equation remains the same, it has x-axis symmetry.

Step 4 ：For y-axis symmetry, replace x with -x in the equation. If the equation remains the same, it has y-axis symmetry.

Step 5 ：For origin symmetry, replace x with -x and y with -y in the equation. If the equation remains the same, it has origin symmetry.

Step 6 ：From the tests, we observe that the equation has x-axis symmetry but does not have y-axis symmetry or origin symmetry.

Step 7 ：Final Answer: The equation \(x+y^{2}=1\) has \(\boxed{x\text{-axis symmetry}}\).