Should I take this risk? If so, how can I persuade my parents?

To begin with, here is some background information.

So I plan to take that test this December. The test is one of the graduation requirements of my school. I study Japanese at a language center, but the teaching speed there is so slow. I mean it isn’t really slow, but it isn’t sufficient to get me ready for the test on time, so I have to do some extra preparation at home.

There is that teacher at the center who also has a JLPT class at home. She is confirmed by a few people at the center to be a good teacher. A few days ago I talked to her about my plan, and she offered to teach me at her home, with a promise that I could be able to take the test in August instead of December! Here are some reason that make the offer tempting:
1. I can’t spend all day preparing at home. My preparation has been delayed many times due to other school work, so it’s better to have someone keep the preparation uninterrupted.
2. I’m not sure if my study method is right, it’s better to have a teacher to guide me.
3. If she was honest, I can get the certificate sooner than I plan. It saves a lot of time since I also have to prepare for some more school requirements.

But here are some reasons why I’m reluctant:
1. My parents paid for the course at the center. They won’t be happy if they know I drop off. It will be like I wasted some money of them.
2. My parents don’t know the teacher, so they will be suspicious about her ability.
3. I myself isn’t so sure about her ability either. I have studied with her for just 2 months at the center. There are people who say she is good but still…

So should I take her offer? And if so how can I persuade my parents that I will take that risk?

P.S: my parents have some misconception about the JLPT and the center’s teaching method. They don’t know that the center only teach so that people can speak, not take any test, so in their mind if I just study hard there I can pass any test.