解：?$(1) $?由題意，可知拋物線頂點(diǎn)?$D$?的坐標(biāo)為?$(12，$??$20)，$?點(diǎn)?$B$?的坐標(biāo)為?$(0，$??$2)$?
∴設(shè)拋物線相應(yīng)的函數(shù)表達(dá)式為?$y=a(x-h)^2+k，$?即?$y=a(x-12)^2+20$?
∵點(diǎn)?$B$?在拋物線上
∴?$2=a(0-12)^2+20，$?即?$a=- \frac {1}{8}$?
∴該拋物線相應(yīng)的函數(shù)表達(dá)式為：?$y=- \frac {1}{8} x^2+3x+2(0≤x≤12+4 \sqrt{10} ) $?
?$(2)$?過點(diǎn)?$C$?作?$CE⊥x$?軸，垂足為?$E$?
設(shè)?$CE=b，$??$AE=a$?
則?$ \begin{cases}{tanβ =\dfrac {a}=\dfrac {2}{3}}\\{tanα=\dfrac b{a+2}=\dfrac 35}\end{cases}，$?解得?$\begin{cases}{a=18}\\{b=12}\end{cases}$?
則點(diǎn)?$C$?的坐標(biāo)為?$(20，$??$12)$?
當(dāng)?$x=20$?時(shí)，函數(shù)值?$y=- \frac {1}{8} ×20^2+3×20+2=12$?
∴能點(diǎn)燃目標(biāo)?$C$?
