How Piecewise-Defined Functions Work
I want to first introduce the concept of piecewise-defined functions, and then explore some often-omitted details raised in some recent questions.
How to Factor a Quadratic: Power Tools
Last time, we looked at the standard algebraic methods to factor a quadratic trinomial. Those methods all involve some amount of guessing and checking, especially when the numbers involved are large; and they only work when there are binomial factors with integer coefficients. These are the methods a teacher usually expects you to use. But …
Three Standard Ways to Factor a Quadratic
Last time, we looked at some non-recommended ways to factor a quadratic trinomial. Here we’ll explore several recommended methods (the basic case, trial-and-error, and ac-grouping), looking into how to do them, and why they work.
“Magical” Ways to Factor a Quadratic
Recently in my college tutoring center, a student factored a quadratic polynomial using the X method, which I had heard of, but never watched being done for a hard example. Here on the site, a teacher recently asked about a related method I know as “slip-and-slide”. Both are “magical”, with no obvious reason they should …
Using a z-Table: Rounding and Interpolating
Last time, we considered what the normal distribution and the z-score mean; here, we’ll look at some more recent questions demonstrating how to use them. In particular, we’ll see basic examples using a table, and then decide what to do when the right number isn’t there.
What is a z-Score, and Why?
Last time we looked at some questions about drawing or interpreting the normal curve (graph of the normal distribution). Let’s back up and consider what it actually is. In particular, we’ll see what the “z-score” means.
What Does the Normal Curve Really Look Like?
We’ll look here at a recent question, and another from a year ago that it reminded me of. I see a lot of inaccurate sketches of the normal distribution, usually from statistics students (in which case accuracy isn’t really important, but can show that you know what you’re talking about), and sometimes elsewhere.
Names of Small Numbers: One to Twenty
Having looked at words for large numbers, let’s turn to the less-asked, but still interesting, question of where our words (in English) for ordinary little numbers come from. We’ll look at the origins of one, two, three, then eleven, twelve, thirteen, and then first, second, third.
Names of Large Numbers: Vigintillion and Beyond
Last time we looked at names of anniversaries (like “semiquincentennial” for the 250th), and other words based on Latin numbers (like “septuplets” for 7 babies). Let’s back up and look at the names in English for large numbers themselves, like million, trillion, and vigintillion. We’ll work up to the big ones!
What is a Semiquincentennial?
This is the 250th anniversary of the United States, and as a result we’ve heard the term “semiquincentennial” a lot. (Well, a lot more than usual.) That reminded me of several past questions about such terms, so we’ll take a look at them now, starting (after a quick introduction) with one asked 25 years ago …