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

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Answer 1 · 2016-12-27T08:20:41

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 $pi=180^o$ .

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