Question

Algebraically determine if the relation x = y2 – 100 is symmetrical with respect to the x-axis, y-axis, or the origin.

A: y-axis symmetry

B: origin symmetry

C: no symmetry

D: x-axis symmetry

Answer 1

Answer: Option D: x-axis symmetry

Explanation:

The symmetry concept can be explained as below:

1. If any point say, (x,y) on the graph, then (x,-y) is also on the graph, it shows x- axis symmetry.
2. If any point say, (x,y) lies on the graph, then, (-x,y) should also lie on the same graph, then is shows y-axis symmetry.

Now, here the graph is for x = y^{2}-100 is attached.

Suppose, (x,y) = (-100,0)

then, solving this point satisfies the equation of given graph.

Also, (x,-y) = (-100,0) satisfies the equation of the given graph.

Hence, the relation x = y^2 – 100 is symmetrical to x-axis.