SOLUTION: Please help determine whether the graph of y = x^2 + 9 is symmetric with respect to the x-axis, the y-axis, or the origin.

Algebra ->  Coordinate-system -> SOLUTION: Please help determine whether the graph of y = x^2 + 9 is symmetric with respect to the x-axis, the y-axis, or the origin.      Log On


   

Question 92023: Please help determine whether the graph of y = x^2 + 9 is symmetric with respect to the x-axis, the y-axis, or the origin.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
determine whether the graph of y = x^2 + 9 is symmetric with respect to the x-axis, the y-axis, or the origin.
--------------
graph%28400%2C300%2C-10%2C10%2C-5%2C20%2Cx%5E2%2B9%29
--------------
To answer the question without graphing check the following:
f(x) = x^2 + 9
f(-x) = (-x)^2+9 = x^2+9
-f(-x) = -[x^2+9] = -x^2-9
------------------
Since f(x) = f(-x) you have y-axis symmetry
Since f(x) does not equal -f(-x) you do not have origin symmetry.
=====================
Cheers,
Stan H.