3. If the parabola $y=x^{2}+b x+c$ intersects the $x$-axis at only one point, and passes through points $A(m, n), B(m-8, n)$, then $n=(\quad)$.
(A) 8
(B) 12
(C) 16
(D) 24
3. C.

According to the problem, we have
$$
\begin{array}{l}
n=m^{2}+b m+c=(m-8)^{2}+b(m-8)+c \\
\Rightarrow b=8-2 m .
\end{array}
$$

Notice that, the parabola $y=x^{2}+b x+c$ intersects the $x$-axis at only one point.
Then $b^{2}-4 c=0 \Rightarrow c=\frac{1}{4} b^{2}=(4-m)^{2}$.
Thus, $n=m^{2}+b m+c$
$$
=m^{2}+(8-2 m) m+(4-m)^{2}=16 \text {. }
$$