Due Monday 9/22

The homework is to finish section 1.5. Some notes on the problems:

• 3 – Replace question 3 with the following: Given the diagram on the previous page, explain why the relationship 2a=|PF1-PF2| is true. The original wording is confusing.
• 4a – You are plugging x’s, y’s and c’s into the distance formula, then plugging this into the hyperbola equation |PF1-PF2| = 2a and then simplifying. The algebra part of simplifying closely follows the procedure you used in problem 1. I suggest you use a separate sheet of paper.
• 4b – Stare at the picture on the previous page until you see why the expression a^2 + b^2 = c^2 is true.
  

A Reference Text

There have been several requests for a reference to a text that could be used to supplement the material we are covering in class. This is the text we have used in the past:

Precalculus – Mathematics for Calculus 4^th edition, Stewart, Redlin and Watson

It is a big blue book. The Upper School library has 4 copies on reserve, the study center has 4 copies, and it is being used in Intensive Precalculus, Precalculus Fundamentals, and Intensive Algebra 2, so many of your classmates have copies. Ellipses and Hyperbolas can be found in sections 9.2 to 9.4.

I encourage you to use this book as a supplement to the class. However, recall that two of the main goals of this course are to (a) learn math content and (b) become more sophisticated thinkers and problem solvers. The only way to become a more sophisticated thinker is to struggle through concepts you don’t understand and try many things that do not work. This is frustrating at first. If you get in the habit of looking up answers in Stewart before making a meaningful attempt to solve it on your own, then both your problem solving ability and your depth of understanding of these topics will suffer. In other words, be sure to use the book as a resource and not a crutch.