# Due: 9/16/2013 (Monday)

# Section 2.1: Completing the square and Extraneous solutions.

### Optional Video: Completing the square review.

We put a lot of time into completing the square last year, but it has been a long summer. This is a video that quickly covers where the method comes from, why the method works (though it is not a proof) and how to use it. All of this in under 15 minutes!

### Section 2.1 Reading:

- Read/skim section 2.1 (p.80 to p.87). You have already seen everything in this section but it is a good idea to just refresh your memory.
- Pay careful attention to example 4 on page 85.
- Review the blue summary box about the Discriminant on page 87.

### Exercise set 2.1

- p.88 #19,33,39,40
**Honors:**You may work with others on this project.- Read this wikipedia article.
- Write a function called
*bad_**quad_solver*in the language of your choice that computes the roots of a quadratic using the vulnerable quadratic formula. Write a test function that demonstrates input for which it works well and input for which it is vulnerable to loss of significance. - Write another function called
*better_quad_solver*that uses a better algorithm to compute the roots of a quadratic. Demonstrate that this function is not vulnerable by calling it with the same arguments that*bad_solver*handled poorly. - Print your code and include it when you turn in your chapter 2 assignments.

### Section 2.2 Reading:

We did all of this stuff last year, so here are some suggestions to help structure your speedy review.

- Read/skim section 2.2 (p.91 to p.100). You have already seen everything in this section but it is a good idea to just refresh your memory.
- Pay careful attention to example 1 on page 91, example 6 on p. 97 and example 7 on page 99.
- Review the property summary box on page 99 about extraneous solutions.

### Exercise set 2.2

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# Section 2.3: Graphical approach to solving inequalities.

This video covers a method that can simplify solving inequalities. Section 2.3 in the text covers other topics as well, but you got loads of practice with that stuff last year. That said, I will suggest a few items to focus on as you read/skim the section as part of your whirl-wind review.

### Section 2.3 Reading:

- The section starts on page 103
- Be sure to review all of the vocabulary from the section. You know it is vocab because it is in
**bold.**Seriously. You should be very familiar with the meaning of all of the vocab in this section! - Some of the trickier questions on SATs (and other hoops through which you will likely find yourself jumping soon) involve a familiarity with the properties in the
**Property Summary**box on page 104. So, maybe you want to just look them over. - Have a look at the theorem about absolute value on page 107. Make sure you are familiar with it. Notice that if you regard |
*u*| as the distance from*u*to zero, then the theorem makes a lot of sense if you graph what it is telling you on a number line. Try it…or read the paragraph directly under the theorem which basically tells you what I just said.

### Exercise set 2.3

- p.110, #1,13,19,33,39 (do these using a graphical method as in the video …for #39 you will have to do a little algebra first. You may use a graphing utility to help you find points of intersection. It is a whole lot easier than the way the authors describe doing #39 huh?)
**Honors:**p. 111, # 44. You may write a program to do part a, if you like.

# Section 2.4: Key Numbers.

### Exercise set 2.4

- p.120, #1-6 all, 11, 30, 35, 45
- p.120 #53, 55 <- Be sure to check out example 5 before you do these. You might be tempted to try to “clear” denominators. Its a trap!
**Honors:**p.121 #80,81 and either 85 or 86.