## Related questions with answers

Question

Determine whether the graph of each function is symmetric with respect to the origin. $f(x)=5 x^{2}+6 x+9$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2To check for $\textbf{origin symmetry}$, we need to replace $x$ with $-x$ and $f(x)$ with $-f(x)$. If we get an equal expression, the function is $\textbf{symmetrical}$ in regards to the $\textbf{origin}$.

$\begin{align*} f(x)&=5x^2+6x+9 \to -f(x)=5\left(-x\right)^2 -6x+9 \to -f(x)=5x^2 -6x +9\\ f(x)&\ne -5x^2+6x-9\\ \end{align*}$

Since we did not get a valid expression, $f(x)$ is $\textbf{not symmetrical in regards to the origin}$.

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