Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.

y^2 - x - 1 = 0

Question

Determine whether the graph of the equation is symmetric with respect to the x-axis, the y-axis, and/or the origin.

y^2 - x - 1 = 0

anonymous · Answer

x-axis

anonymous · Answer

This is symmetric about X-axis as both positive and negative inputs to y are giving same output to x

ybarrap · Answer

y^2 - x - 1 = 0
y^2 -1 = x
x = y^2  - 1
Note that both positive and negative values of y give the same x, visually this means that there are two values of y that give the same x. The value of y for each x will be "reflected" about that value of x, this is true for each vale of x.  

So this reflection is a property of the symmetry of this equation about the x-axis