题干

(本小题满分12分)
在平面直角坐标系xOy中,抛物线的解析式是y =+1,点C的坐标为(–4,0),平行四边形OABC的顶点AB在抛物线上,AB与y轴交于点M,已知点Q(xy)在抛物线上,点P(t,0)在x轴上.

(1) 写出点M的坐标;
(2) 当四边形CMQP是以MQPC为腰的梯形时.
① 求t关于x的函数解析式和自变量x的取值范围;
② 当梯形CMQP的两底的长度之比为1:2时,求t的值.
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