已知二次函数的图象的顶点在原点O，且经过点A（1，$\frac{1}{4}$）．

（1）求此函数的解析式；

（2）将该抛物线沿着y轴向上平移后顶点落在点P处，直线x=2分别交原抛物和新抛物线于点M和N，且S_△PMN=$3\sqrt{2}$，求：MN的长以及平移后抛物线的解析式．

    Hello，I'm Lily．I have a big and happy family．My father，Jack，is a maths teacher．He has black glasses．He is in the living room now．My mother，Judy，is tall and thin．She has long hair．Where is she? Ha—ha，she is in the kitchen．She can cook yummy food．

    Who's this girl? She has a blue hat．Yes，she's my baby sister，Lula．She is watching TV in the living room．I have a brother，too．His name is Ben．Ben is fat，he likes candies very much．It's not good．Do you see my little puppy? His name is Mimi．Look，he is in the bedroom with Ben．"Would you like some candies?" Ben asks．

    Guess，where am I? In this room，you can see a computer on the desk．Near the desk．It's my schoolbag．A blue chair is near the desk，and I can sit on it and read many books．I like stories very much．And I have twenty storybooks on my big desk．Yes，I'm in the nice and big study．

    I love my family!

⑴读短文，选择正确图片；⑵⑶⑷⑸⑹⑺判断正误。

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