Algebra II

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Determine whether the grapg of the given equation is symmetric with respect to the x-axis, y-axis, and/or the orgin.

f(x)=3x²+1

x²+y²=81

1. Damon

f(-x) = 3 x^2 + 1 = f(x)
so it is even, symmetric about y axis
it is a parabola with vertex at (0,1) and opening up
Not symmetric about x axis or origin

f(-x)= f(x) = (-x)^2 + y^2 = x^2 + y^2
also symmetric about origin (x^2+y^2) = distance from origin^2 = 9^ 2 = constant
It is a circle with radius 9 and center at origin

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