Ans: A
Write the equation of the graph to the general form and vertex form.
$\begin{array}{rcl}
y & = & (m-x)^2 +n \\
y & = & (x-m)^2 +n \\
y & = & x^2 -2mx +m^2 +n
\end{array}$
I must be true. The coefficient of $x^2$ is 1, which is positive.
II may not be true. The $y$-intercept of the graph is $m^2 +n$. It can be negative is $m =1$ and $n=-3$.
III may not be true. Sub $x=n$ into the right side of the equation, we have
$\begin{array}{rcl}
\text{RS} & = & (m-n)^2 +n
\end{array}$
Which may not equal to $m$.
