Question

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

Answer 1

Not symmetric about O.

Explanation:

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`.