Answer
See below.
Work Step by Step
If $x$ is even, then: $ax^2$ is even, $bx$ is even and $c$ is odd, thus $ax^2+bx+c$ is odd.
If $x$ is odd, then: $ax^2$ is odd, $bx$ is odd and $c$ is odd, thus $ax^2+bx+c$ is odd.
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