In this case what is the inverse of
y = -4x² + 2 ?
Due to my math experience I looked at the multiple choice answers and knew which one it had to be...however due to my carelessness when I tried to show him why I got the wrong answer because I left off a negative when I copied down the problem. We did the problem more than once and this vid shows the last time we did it.
Two principals here:
One: NEVER TRUST THE TEACHER.
Two: You aren't wrong you are just getting more information.
Too many parents (and some teachers) are afraid to work with their kids because they might get it wrong and be embarrassed or what have you. Just get to work and see if you can get the answers...sometimes it's good to get the answer first and then look at the problem. I have had more than one student say it's easy when you know the answer. That's true and then with the thought this is easy you can see how to solve the problem and you know where you are going.
Another thing with some multiple choice tests: you can see answers that reflect common mistakes or misunderstandings of concepts that would lead you to pick the wrong answer. Talk about them. Talk about why they would put that answer as a choice on the test. This often helps deepen understanding.
Now in order to learn how to do these it requires more than on 3 and a half minute video. They can get the rule "just switch the variables and solve" but they will forget the rule in just a few weeks...
You need at leaste three examples of which this would be one of the last ones. They should have also spent some time understanding the basic concepts of Hero Zero and No Fun Get Back To One. (HZ & NFGBT1)
Here is the first example I showed this particular student:
y = x² therefore the inverse would be y = ± √x
First we "swap" the variables: x = y² which is the same as y² = x and solve (NFGBT1) by "square rooting" both sides: y = ± √x
Then you just make them slightly more complex: y = x² + 1 etc...
"Example isn't another way to teach, it is the only way to teach." ~AE
More at the house of math.