Three points

Suppose you are given the three ordered pairs (6,4), (-1,-3), and (2,-4) shown below.  Find equations for as many curves as you can that are uniquely defined by these three points.

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How many zeros?

This is our first week back in school during which our students have been learning aspects of their new handheld  (TI-Nspire CAS) and online (Wolfram Alpha) CAS in the context of enhancing their problem-solving ideas.  While exploring the capabilities of these amazing computational tools, one student entered a number like 300! (That’s factorial) and was pretty impressed to see all of the digits listed.  Before going further, I asked

  1. how they might determine the number of digits in 300!,
  2. what the final digit was, and
  3. how many of that final digit were in an uninterrupted sequence at the end of an expanded representation of 300!.

We’ll give a few days for your ideas before posting our students’ thoughts.

Solutions are here.

PreCalculus Transformed — Published!

Pre-Calculus Transformed highlights the under-explored role of transformations in visualizing, interpreting, and understanding pre-calculus concepts. This text develops function composition to expand transformations far beyond constant translations and dilations. Students discover underlying patterns, bring out connections between otherwise seemingly unrelated ideas, and learn to more easily analyze problems that initially appear complicated. Overall, this text provides an interconnected and dynamic pre-calculus experience with a wide range of problems from basic practice to those requiring creativity, insight and meaningful connections.

While Pre-Calculus Transformed integrates computer algebra system (CAS) technology throughout, its concepts can be grasped without a CAS. However, routine CAS use in the text enables students to investigate, recognize patterns, and make broader predictions about function behavior, while appropriately maintaining their focus on critical problem characteristics without losing themselves in algebraic manipulations that are explored independently elsewhere.