Tim Corica

P.S. The sum/product formula is easy to prove using (x+r1)(x+r2), and yields a quick corollary that if we have real coeffs (1) the sum is real, which means a+bi pairs with c-bi and (2) the product is real, which for these pairs only works if a = c, that is, conjugates.

3/2 😉

I posted about using sum/product of roots, which still seems more useful and elegant to me. But this last idea (shifting by 3) is very cool.

My strong preference would be to have developed x^2-(r1+r2)x+r1r2 in prior work. Then we get b=-[(-3+i) + (-3-i)] and c=(-3+i)*(-3-i) both of which are easy to compute: b=6 and c=10.

x^2+6x+10

2/2

IF the goal is to practice algegraic manipulation, then I'd multiply (x-(-3+i))(x-(-3-i)), trying to use each root as a block, rather than expanding and multiplying trinomials. HOWEVER, ..... (1/2)

401,000 people moving state to state in fear of having legal documents invalidated (KS), jail time for using restrooms (FL, UT), loss of access to adult care (dozens) or youth care (dozens even in D-led states), & the message from “opposition” is still largely “you’re making too big a deal of this.”

Way below, tbh.

Thx. Your link says something quite different: the %age of the stock of "large homes" owned by Boomers (empty nesters) vs Millenials (not GenZ) in 2022 when GenZ were younger, and says nothing about second homes.

My quick research: GenZ 27.1% own homes; GenZ is 14-29. Boomers 17% own a 2nd home.

I understand the concern, but is this statement factually accurate? Can you post a link to the information this is based on? Has it changed in 2026?

Graph showing people's estimates of probability for various phrases.

What does "likely" mean, in terms of probability? This article looks at the question - I think it would make a great class exercise, where students give their own answers, and then read the article. #iTeachMath #MTBOS

www.thetimes.com/uk/science/a...

BREAKING

Former ICE agent:

On my first day training new cadets, I received secretive orders to teach them to violate the Constitution by entering homes without a judicial warrant.

Wow! Nice (quick) work!

Understand. Could you slip problem #1 into an assignment, and then slip #2 into a later assignment? I.e., fold it into your work rather than take time?

1. Our system of time measurement, with 60 minutes in an hour and 60 seconds in a minute originated with the ancient Sumerians in the 3rd millennium BC. They used a base 60 (rather than base 10) system, and this also explains why we define one “degree” as 1/360 of a circle. a. Sometimes people give a time as 1.5 hour. How many hours, minutes and seconds is this? Write your answer as HH:MM:SS. b. Suppose a video is 0.2 hours. How many minutes and seconds is this? c. Suppose some strange instructions for a cake specify baking for 2.23 hours. How many hours, minutes, and seconds is this? If it is not an exact number of seconds, include decimals on the SS value. d. A movie is 95 minutes and 34 seconds. Give the length of the movie in HH:MM:SS form, and then give the length in hours, using decimals as needed. 2. We have written angle measures in decimal format (e.g, 32.5 degrees). However, there are occasions (often in navigation) where angle measures are written in degree:minute:second format. There are 60 minutes in a degree and 60 seconds in a minute. For example, an angle of 33.5 degrees might be written in DD:MM:SS form as 33:30:00. a. Write 1.5 degrees in this format. Write 0.2 degrees in this format. b. Suppose an angle is 63.25 degrees. Write this in DD:MM:SS format. c. Suppose an angle is 40 degrees, 10 minutes, and 15 seconds. Write this as a single value in degrees, using decimals as needed.

Here's an option: Use something like this as part of a homework or a group work assignment. The goal is to avoid making DMS sound weird and something you have to be taught. Rather, it's just an idea that you can certainly figure out. Avoid "teaching" it.

Love this!

Quakertown parents, groups demand release of students in police clash Civil rights groups and parents gathered in front of the Quakertown Police Department Saturday demanding answers for the violent confrontation Friday.

INBOX: the police chief of Quakertown, Pa., led a group of plainclothes officers to disrupt a peaceful high school student sidewalk protest yesterday.

They threw an underage girl to the ground, choked her, and disconnected all calls to the detention center where she and others are currently held.

‘Don’t go to the US – not with Trump in charge’: the UK tourist with a valid visa detained by ICE for six weeks Karen Newton was in America on the trip of a lifetime when she was shackled, transported and held for weeks on end. With tourism to the US under increasing strain, she says, ‘If it can happen to me, i...

So why did ICE detain her, and keep her locked up for so long? As Karen got to know the guards at the Northwest ICE Processing Center where she was held, she kept hearing the same thing from them: that ICE officers are paid a bonus every time they detain someone. www.theguardian.com/us-news/2026...

I tried, I really tried, to watch this. I lasted only 5 minutes. I think "I was being a good boy" was the last straw for me.

I think it makes arithmetic ops a bit simpler at times, and it can lead to simpler exprs (e.g., 10/sqrt(5) vs 2 sqrt(5) ). But it's a fussy convention and adds to students' belief that math is just a bunch of arbitrary rules to be mastered, rather than a way to find, and state, truth.

Fantastic post! (FWIW, the word "ordnance" in the caption of the first photo is misspelled as "ordinance".)

NEW: DOJ told a judge in New Jersey that it had violated court orders about 54 times between Dec. 5 and this week — the latest accounting of a phenomenon that used to be rare and is now rampant. www.politico.com/news/2026/02...

Sorry to report that @paddymacmahon.com ‘s pretty diagram caught my eye as it passed by my scroll, so I failed to attack it on my own! A glance at the two radii gives it away, and when I worked the algebra it was chef’s kiss.

Wow!

Curious about the capitalization. Joules, Newtons, etc. are all capitalized when abbreviated, but not when written out. 4 joules is 4J. I don't think I ever noticed, but it's kWh because of James Watt. A counter-example that proves the rule is ohms. It would be strange to say 10 O so we say 10 Ω

Let’s not teach them how to solve this. Let’s teach them about lines and gradients and then give them this problem to work on in small groups. Then each group can present their process. If desired, you could end with a comparison of different methods based on efficiency, elegance, directness, etc.

In the U.S. the term "vertex" for a parabola is pretty universal. I have generally only seen "turning point" used to refer to relative extrema in higher order polynomials.

Why “turning point” and not “vertex”? Is that the preferred terminology where you teach?

Mine are pretty good about this. I’m giving support for kids in PreCalc, AB/BC Calc, AP Physics 1, and some CS.

Made my donation to ILCM. Thank you for posting this thread.

I don’t really know what I expect in posting this, but maybe some people see it and can learn from it.

I’ll call it “lessons from an unwilling immigration attorney.”

1/

Yes. Dan Goldman used it on Chris Hayes tonight and I had the same reaction.