Linear Regression and Interpretation of Results

Hey kids! Hopefully you’re noticing that I am starting to upload videos involving old topics. –Not a coincidence. Those are the topics that I think are most important for this year.

Here is a video on linear regression and (MORE IMPORTANTLY) the interpretation of each part of equation: (7 minutes and 46 seconds)

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Minimizing Surface Area

I pulled together a video on how to minimize surface area using the graphing calculator. The same method can be generalized for any shape or for maximizing / minimizing any geometric quantity. This idea of optimization is very important in Calculus! (6 minutes and 20 seconds)

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Arithmetic and Geometric Series

Since it looks like you guys need some reminders on how to evaluate arithmetic and geometric series (from Ch. 1), here are two videos that I made that go over just that:

Evaluating an arithmetic series (5 minutes and 47 seconds long)

Evaluating a geometric series. In this video I made a small mistake in my oral explanation. Can you catch it? (It’s not enough to “mess you up.”) This video is 4 minutes and 38 seconds long.

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Completing the Square for Vertex Equation

Since completing the square has a lot of steps and it’s easy to forget some of them after a while, I went back and made a video for this topic.

See (5 minutes and 7 seconds)

It shows how you go from a standard quadratic function equation into the vertex form, assuming that you are familiar with the expansion “shortcut” that (x + a)2 = x2 + 2ax + a2.

By the way, are you having trouble streaming the videos? If so, try pausing it as soon as it starts to auto-play, and waiting a few minutes before you return to the computer to view it. Generally, video files that stream over the internet are already in formats that allow you to load them quickly, so it shouldn’t take more than a few minutes to load each video.

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Function Transformations

Here’s a video for an earlier topic: function transformations. (I am going to go backwards and make the videos for the trickier old topics.) I apologize in advance for the choppiness of my explanation. You can still follow it, and the work I am writing down is all correct, but there are a couple of parts when the explanation is a bit awkward. Also, I should have highlighted in the end that the graph got flipped horizontally because of the negative sign on the inside. (7 minutes and 45 seconds long)

Again, this one is one that I recommend you doing alongside the video, pausing when necessary.

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Composition Functions – How to Find Their Domains

Here is a video that goes over how to find the domains of composition functions. I showed in the previous video how to get these composition formulas, so this video only discusses the domains of those results. (7 minutes and 8 seconds long)

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Composition Functions – How to Write Their Equations

Here is a video about how to write the function equations for composition functions
(f o g)(x), (g o f)(x), and (g o g)(x). (6 minutes and 50 seconds long)

Note: This will be followed by another video (soon!) that shows you how to analyze the domains of these composed functions.

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