Example?. The following are rough sketches of the graphs of two quadratic functions:
$$
\begin{array}{l}
y=a x^{2}+b x+c \\
y=p x^{2}+q x+r
\end{array}
$$
(i) Based on the graphs, determine $p, q, r, a+c, pa^{2}+qa$
(ii) Let the x-coordinates of the intersection points of the two graphs be $\boldsymbol{\alpha}, \boldsymbol{\beta}$, express $\alpha+\beta, \alpha \beta$ in terms of $a, b, c, p, q, r$.