#### Answer

$-\frac{p^{2}}{9}+\frac{4p}{3}+1$

#### Work Step by Step

We are given that $g(x)=-x^{2}+4x+1$. In order to evaluate the function at $x=\frac{p}{3}$, we can plug in $\frac{p}{3}$ to the function and evaluate directly.
$g(\frac{p}{3})=-x^{2}+4x+1=-(\frac{p}{3})^{2}+4(\frac{p}{3})+1=-(\frac{p^{2}}{9})+\frac{4p}{3}+1=-\frac{p^{2}}{9}+\frac{4p}{3}+1$