Answer
$-\frac{1}{16}$
Work Step by Step
We are given that $g(x)=-x^{2}+4x+1$. We can plug the given value into the equation and evaluate.
$g(-\frac{1}{4})=-(-\frac{1}{4})^{2}+4(-\frac{1}{4})+1=-(\frac{1}{16})+(-1)+1=-\frac{1}{16}-1+1=-\frac{1}{16}+0=-\frac{1}{16}$
