Find the value of the polynomial $x^{2}-7x+12$ at $x=\frac{1}{2}$.

(A) To find the value of the polynomial $p(x) = x^{2} - 7x + 12$ at $x = \frac{1}{2}$,we substitute $\frac{1}{2}$ for $x$ in the expression:
$p(\frac{1}{2}) = (\frac{1}{2})^{2} - 7(\frac{1}{2}) + 12$
$p(\frac{1}{2}) = \frac{1}{4} - \frac{7}{2} + 12$
To add these,find a common denominator,which is $4$:
$p(\frac{1}{2}) = \frac{1}{4} - \frac{14}{4} + \frac{48}{4}$
$p(\frac{1}{2}) = \frac{1 - 14 + 48}{4}$
$p(\frac{1}{2}) = \frac{35}{4}$
Converting the improper fraction to a mixed number:
$\frac{35}{4} = 8 \frac{3}{4}$