How do you determine whether the graph of #f(x)=5x^2+6x+9# is symmetric with respect to the origin?

1 Answer
Dec 27, 2016

Not symmetric about O.


The graph of y = f(x) is symmetric with respect to the origin, if f(-x) = -

f(x) =-y. In other words, if (x, y) is on the graph, (-x, -y) has to be on

the graph.

Here, f(x)=5x^2+6x+9 and f(-x)= 5x^2-6x+9 that is not #-f(x)#. So, the

graph is not symmetric about O.

In polar form #r = f(theta), f(theta+pi)=f(theta)# is the condition for

symmetry about the pole. In other words, f(theta) should be periodic

with period #pi=180^o#.