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某隧道根据地质结构要求其横截面要建成抛物线拱形，计划路面水平宽度AB=12m，根据施工需要，选取AB的中点D为支撑点，搭一个正三角形支架ADC，C点在抛物线上（如图所示），过C竖一根立柱CO⊥AB于O． （1）求立柱CO的长度； （2）以O点为坐标原点，AB所在的直线为横坐标轴，自己画出平面直角坐标系，写出A、B、C三点 的坐标（坐标轴上的一个长度单位为1m）； （3）求经过A、B、C三点的抛物线方程； （4）请帮助施工技术员计算该抛物线拱形的高．
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