# 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!

• 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.
• 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.

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.

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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.

• 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.