分析:
(1)根据已知的与x轴的两个交点坐标和经过的一点利用交点式求二次函数的解析式即可;
(2)首先根据上题求得的函数的解析式确定顶点坐标,然后求得点C关于x轴的对称点的坐标C′,从而求得直线C′M的解析式,求得与x轴的交点坐标即可;
(3)
①如果DE∥OC,此时点D,E应分别在线段OA,CA上,先求出这个区间t的取值范围,然后根据平行线分线段成比例定理,求出此时t的值,然后看t的值是否符合此种情况下t的取值范围.如果符合则这个t的值就是所求的值,如果不符合,那么就说明不存在这样的t.
②本题要分三种情况进行讨论:
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/faedab64034f78f09d7f255a7b310a55b3191c26?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/bf096b63f6246b60b07b0ddde9f81a4c510fa226?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
∴不存在PQ∥OC;
②分情况讨论如下,
情况1:0≤t≤1
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/d6ca7bcb0a46f21f091ae0faf4246b600c33ae69?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)