#### Answer

$g(-\frac{1}{4})=-\frac{1}{16}$

#### Work Step by Step

To find the value of $g(-\frac{1}{4})$, substitute $-\frac{1}{4}$ to $x$ in $g(x)$ to obtain:
$g(x)=-x^2+4x+1
\\g(-\frac{1}{4})=-(-\frac{1}{4})^2+4(-\frac{1}{4})+1
\\g(-\frac{1}{4})=-\frac{1}{16}-1+1
\\g(-\frac{1}{4})=-\frac{1}{16}$