Such a great question! No worries. I said at that point "as you have before," meaning I was assuming that students already had experience "factor a perfect square trinomial." There are some good videos of you search for that exact phrase. Here's the basic idea: Suppose I square (3x + 2). Inother words, multiply (3x + 2)(3x + 2). As you probably know, that will give you 9x^2 + 12x + 4. But how can I go the other way, in other words, factor the perfect square trinomial 9x^2 + 12x + 4? (Side note: How did I know it's a perfect square trinomial? Experience tells me that if I square root the 9 and 4, so I get 3 and 2, multiply those and double the answer, it's a perfect square if that number matches the 12 in the middle. So, 25x^2 + 30x + 9 is a P.S.T. and 16x^2 + 20x + 1 isn't.) Back to factoring: I know 4x^2 + 20x + 25 is a P.S.T., so now just write it up in this form: (px + q)^2. p is always the square root of the first coefficient, in this case 2. q is always the square root of the last coefficient, in this case 5. So the factored form is (2x + 5)^2. So 9x^2 + 42x + 49 (it's a PST) is (3x + 7)^2 x^2 + 16x + 64 (a PST) is (x + 8)^2 Note: the first coefficent is 1. And, from the problem in the video, x^2 + 10x + 25 factors to (x + 5)^2. Best of luck, Dan

Thanks. I enjoy what I get to do, and I'm glad I can be helpful beyong my classroom walls.

My pleasure. I know it's old, but it still seems to be helping people.

I'm very glad to be able to help

Well hey at least you knew you needed to rehydrate! Your brain and body will stash that experience away as something to try to avoid in the future, so it wasn't a wasted experience.

Oh, man! I hope it went well!

@@djnechodom yeah i missed like 2 pages:/

I'm glad the videos were helpful. I know they're old, and they're not very fancy, but I find that some people just want to have things explained to them simply. Best to you.

Wow! I'd be interested in your story about that. That could be good information for me to share as a coach. Are you willing to share more?

@@djnechodom It took me 2 years. I took a supplement that caused diarrhea for weeks and went into dehydration shock. My potassium and salt went super low and I didn't correct it quick enough. It turned chronic and I could not bring my cellular salts or fluid up any quicker, so I suffered ongoing severe dehydration symptoms for 2 entire years. Raised my potassium by one number every 4 months on a hair analysis tracking test. You simply cannot push something into the blood and expect it to go to the cells immediately. That's not how it worked for me at all. If you want dehydration corrected quickly, it has to be lost AND regained on the same day. The longer you stay dehydrated, you will not be able to fix it quickly and it will become a nightmare.

@@JH-nb4nn Wow, I'm really sorry that happened. I will use your story as another point of emphasis as I encourage athletes to learn to monitor and care for their bodies.

@@djnechodom thank you :-)

Sorry, let me see if I can help. That part of the video starts at 2:13. Here's the basic idea: * I already know that the equation look like this: y = 3x + b, I just don't know what goes in for b. (Did you catch why I put the 3 there? In the equation y = mx + b, the slope is m and the b is the y-intercept. I already found out the slope is 3.) * The reasoning I use is this: When it's all said and done, the equation has to "work" for any given point that's on the line. In this case, I know that (6,6) is on the line, and so is (4,0). When I say it has to "work," I mean that if I put in the x-coordinate for x and calculate, I have to get the y-coordinate. So in the final equation, I have to be able to put in 6 for the x and get 6 for the y. Or, I have to be able to put in 4 for the x and get 0 for the y. In the video, I put in 6 for the x, multiplied it by the slope of 3, then asked what b has to be in order to get 6 for y. It would look like this: 6 = 3(6) + b, 6 = 18 + b, now solve for b by subtracting 18 from both sides, so -12 = b. I could also use the other point (4,0). I'd put 4 in for x, then ask what b has to be so I get 0 for y. 0 = 3(4) + b, 0 = 12 + b, solve for b, -12 = b. Either way, no in the equation y = 3x + b, I know that b = -12. The final equation is y = 3x + -12, or y = 3x - 12. I hope you can make some progress. I know this stuff is really frustrating when it comes at you fast, and it's worse when guys like me talk about like it's supposed to be easy. Actually, it often sucks for long time until your brain adjusts to it.

@@djnechodom ohhhh ok, thank you very much,. I kinmd of found out how to do the equation on Friday, but thank you for still checking up.

No kidding?! Congratulations on your upcoming marriage. Who's your fiance'?

That's an excellent question! Yes, we measure in pints! Also my measurement tends to be on a scale of "Does it taste good, or is it like the typical combination of mule piss and goat vomit that passes for American store-bought beer?"

You're welcome! I tell my athletes all the time, "Hydrate or die-drate!"

@@djnechodom thank you, didn’t get better after hydrating, went to doctors and found out I had the flu, just now getting over it.

No worries. I wasn't meant to be good, it was meant to clarify some things that my students were struggling with at the time. I hope you got the answers you needed from somewhere.

I'm so sorry I didn't see this earlier. I hope you got your question answered in some way. I would find the midpoint of BC if I was finding the equation for a 'median,' which goes from a vertex to the midpoint of the opposite side. Since I'm find an 'altitude,' which intersects the opposite side at a right angle, then the midpoint isn't relevant. Best to you.

same

You're very kind. I'm glad you found the video helpful.

Good news. I'm glad it was helpful. Feel free to comment back if you've got questions.

Glad it was helpful. I'm still teaching (32nd year) and still trying to help people make sense of this stuff.

Hey, I'm glad to be able to help. Nothing wrong with stuff being hard, as long as you keep pushing forward. Best to you.

Wow! I'm honored to have been able to help. Best to you.

Oh, I had volume off! I hear you say that at the end. Thanks!

@@JordanKennison No worries. You could interpret my comment at the end as either 1) I don't want to distract you from the main point of the video, or 2) I'm too lazy to finish out this problem, or 3) I'm using the free version of the screen capture software and I'm close to the end. I'm not sure which would be most accurate. I hope it was a help.

The only thing that didn't work was your parents marriage

@@velhaw8737ohh me personally I wouldn’t let that slide

I'm so sorry I didn't see this earlier. Did you get the help you needed?

If you didn't, I can help. Reply back. At the very least, I can tell you that you'll do the same thing as I showed here, it's just that the fractions make it LOOK more complicated. Don't be embarrassed if you need to review how to add, subtract, multiply and divide fractions.

Sorry to hear that. I don't know anything about your teacher, so it wouldn't be appropriate for me to criticize. But I can tell you a few things you could do to help him at least do a better job teaching YOU. 1. Try to arrive with at least a neutral attitude. I know we teachers are supposed to set the tone for the class, but we're humans and still feed off the energy in the room. If enough people are negative and critical, it drags us down at times. 2. Ask questions. Believe me, these days it doesn't take much to stand out as a "great student." If all you do is ask a clarifying question or two once in a while (Can you tell me again why you factored 2 out of the parentheses? or I'm not sure I understand why you flipped the slope over and made it negative.) you'll seem like a student who wants to learn. It's a sucky deal sometimes, but sometimes even the best teachers put a bit more effort into helping those people understand. 3. Say "Thank you." Seriously. Those two words make a huge difference. Not only to the person who receives them, but also to the one who says them. They even begin to affect others who hear them. Take some deep breaths, be well, and I hope you can find enjoyment in the world around you, maybe even in the wonder and beauty of mathematics. DN

Or does it only work on the two endpoints of the median?

Same

No worries. Happy to help.

@@djnechodomthat’s weird why aren’t you uploading another video?

@@UltimateEnemies2385 It's a little tougher for me now. I moved to a different school and don't have access to the digital white board I had earlier. Could still do them, but they wouldn't look as nice. Did you need help with a particular type of problem? I could cobble something together and tag you.

Hope it helped! It's Saturday night where I live. Are you really studying?!

I'm sure those other factors make a difference, but I'm guessing that the differences aren't major. I would think that the biggest factor would be weight. It would be interesting to see how differences in fat/ muscle ratios change it. (Please note: I'm GUESSING! I'm no expert, nor have I researched this more.)

My rather unscientific rule of 5 big swallow might still work here, since a bigger person would probably take bigger gulps. My biggest point was to encourage my students and athletes to meter their intake rather than thinking they'll rehydrate well by guzzling a full Gatorade.

Yeah, I can see that. I tell athletes that it really depends on what they're doing. If they're doing long workouts where they need electrolyte and fuel stores refilled quickly, then Gatorade is a good idea. If not, then drinking water will keep you hydrated and your food will resupply electrolytes and fuel. But I'm just an old track coach. Plenty of people know more than me.

Keep in mind though that gatoraid is high in sugar. That is unhealthy in the long run. I think health experts down play the health affects of sugar. Electrolytes are just salt. Gatoraid is water, sugar, and salt. I like to add a little salt to my water after a crazy cardio day.

​@@GuyFromTheSouthnot true. Glucose is actually essential to stimulate the hydration. When my mother got chemotherapy she also got electrolye water through an IV WITH glucose

Yeah, you can do the whole thing multiplying the matrices by hand. I chose to use the calculator to save time. You'd need to look up how to find the inverse of a 2x2 matrix, and how to multiply by hand. (Honestly, I can't remember if I made any of those videos, but there are good ones out there.)