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

Dec 27, 2016

#### 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 $- f \left(x\right)$. So, the

graph is not symmetric about O.

In polar form $r = f \left(\theta\right) , f \left(\theta + \pi\right) = f \left(\theta\right)$ is the condition for

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

with period $\pi = {180}^{o}$.