Warm-up

Please complete the student survey. You will have 10 minutes.

Hi, I'm Mr. Leichner! (pronounced Lie-sh-ner)

http://goanimate.com/go/movie/0VfELXWvphiU?utm_source=emailshare&uid=0T3OKGjgsrT8

Notebook Setup:Number each page (front and back) in the bottom corner. There are 140 total pages.

Collaboration (pg. 3)

A HUGE part of our learning in Algebra 2 will be through collaboration with your classmates.

What factors will help make group work effective and productive? Take 3 minutes to discuss - then we will share out.

CollaborationIn Algebra 2, a lot of our group work will involve group roles. The roles will be: Leader, Recorder, Timekeeper, and Culture Keeper. Sometimes I will assign them by number, and sometimes you will choose, but it is important that everyone becomes skilled at every role.

How might group roles contribute to a group's effectiveness? Discuss for 3 minutes and we will share.

Collaboration

Group Norms are important to ensure that groups work productively. Together, we will develop some group norms for the class. What procedures, actions, and techniques would help groups function effectively? Discuss for 3 minutes, and then we will share out.

Whole Class Small Group

Warm-up

Diagnostic Test - we need to see where you are!

VocabularyFunction -

x-intercept -

y-intercept -

Minimum Value -

Maximum Value -

IntervalIncreasing -

Decreasing -

Is It a Function?yx

-4

-1

1

4

2

0

2

10

yx yx

0

1

2

2

0

1

2

2

-5

0

5

10

3

-4

5

5

Function Activity

Write the first letter of your first name NEATLY.

If you put the letter on a graph, would it be a function?

Identifying Key Values

On these graphs, pick out the:

1) x-intercept(s)2) y-intercept(s)3) max/min values4) Interval Increasing5) Interval Decreasing

1) x-intercept(s)2) y-intercept(s)3) max/min values4) Interval Increasing5) Interval Decreasing

1) x-intercept(s)2) y-intercept(s)3) max/min values4) Interval Increasing5) Interval Decreasing

10

-10

50

-50

The Write Time

Why does the vertical line test determine if a relation is a function?

Warm-up

If f(x) = x , g(x) = x , h(x) = x , and j(x) = x,find:

a) f(-17)

b) g(10)

c) h(-3)

d) j(64)

2 3

Graphing 6 Basic Functions

ArgumentationCompare and contrast the similarities and differences between the representations of minimum values, maximum values, and intercepts in equations, graphs, tables, and word problems. Explain which representation gives the clearest representation of each and why.

Warm-up

x and y Intercept Discoveryhttp://secondaryalgebra2.cmswiki.wikispaces.net/file/view/x+and+y+intercept+discovery.docx

Interpreting Word Problems

Two baseball players tracked the paths of their most recent home runs using quadratic functions. The height of one player's baseball modeled the function h(t) = -16(t - 4) + 3, and the height of the second player's baseball modeled the function h(t) = -16(t - 4) + 5. What are the similarities and differences between the graphs? What do those similarities and differences represent in a real-world context?

2

2

Two baseball players tracked the paths of their most recent home runs using quadratic functions. The height of one player's baseball modeled the function h(t) = -16(t - 4) + 3, and the height of the second player's baseball modeled the function h(t) = -16(t - 4) + 5. For each ball:a) What is the x-intercept?b) What is the y-intercept?c) What is the maximum value?

2

2

Using the Calculator to Solve

Finding Key Points in the Calculator

f(x) = ½ (x + 3) + 22

Try Some!

1. For f(x) = -x + 5x - 19, find:

a) y - intercept

b) x - intercept

c) max/min value

d) intervals where increases/decreases

232) With the recent recession, home prices have started to fall. The average sale price of a home since 1900 can be modeled by the formula:y = -2x2 + 216x + 4,000.

a) What was the average sale price of a home in 1900?

b) What year saw the highest average sale price for homes?

c) What was the highest average sale price for homes?

d) When will the average sale price for home be nothing? Determine the feasilibility of this answer.

Independent/Group Work

pg. 88 # 19, 24pg. 89 # 7

Argumentation

Find the y-intercepts of f(x) = 2, f(x) = 0.5(2), and f(x) = 4(2)? Based on the value of f(0) in each function, explain the rationale for the difference in y-intercepts. Use the pattern to form a hypothesis involving the y-intercept of an exponential function.

x xx

Warm-up

1) -12 + 10 2) -12 + 10 3) -12 + 10

4) -3 - 4 5) -3 - 4 6) -3 - 4

Review: Graphing Points

Graph points:A(-4, 2)B(3, 1)C(0, -3)D(-2, 0)

Argumentation

Based on the results of the Absolute Value Discovery, attempt similar transformations for either the quadratic function f(x) = x, the cubic function f(x) = x, or the exponential function f(x) = 2. Analyze and explain the rationale for why the transformations apply to this (and other) functions.

2 3

x

Warm-upBased on the transformations rules and the parent functions you havediscovered, graph:

1) f(x) = (x + 2)2

2) f(x) = x - 3 + 4 3) f(x) = x + 1 - 2

Discovery Discussion

Independent/Group Work

Workbook pg. 50 Allpg. 83 #9, 10

Argumentation

Why do values inside the function move horizontally while values outside the function move vertically?

Warm-up

Domain -

Range -

Define domain and range in your own words.

Domain in the Real World

The summer before going to college, a student earned a promotion to shift supervisor at her job at Starbucks! The new position pays $10.20/hour. If the student's paycheck was modeled by a function, what would be the domain and range? Explain your answer. Why is this domain and range different than other similar functions?

x represents _________________

y represents _________________

Finding Domain of Mathematical Functions

What are the domain and range of:

f(x) = x f(x) = x

f(x) = x f(x) = 2

f(x) = x f(x) = 1x

2

3

x

Domain of Rationals and Radicals Discovery

Based on the domains of f(x) = x and f(x) = , what are the domains of:1x

1) f(x) = x + 2

2) f(x) = x + 2

3) f(x) = 3x - 18 + 7

4) f(x) = + 2

5) f(x) =

6) f(x) = - 9

1x

1x + 2

102x - 5

Independent/Group Work

Write an algebraic function with a domain of:

1) x > 4

2) x < 3

3) x = 0

4) x = -4 5) x = 5

The Write Time

Why do radicals and fractions restrict the domains of functions?

Warm-up

Find the domain for the following examples:

1) f(x) = 3x + 62x - 8

2) f(x) = 4 -2x + 3 + 4x

3) A t-shirt vendor charges $8/t-shirt with a minimum order of 25 shirts.

4) On any section of the SAT, a student can score between 200 and 800, inclusive, in multiples of 10.

Argumentation

Create graphs of functions with the following domains: {All real numbers}, {All real numbers for x 0}, {All real numbers for x 0), {All real numbers for x < 0}, {All positive integers}, and {All integers}.1. How do your graphs accurately represent the required domains?2. What are the similarities and differences between your graphs? 3. For each graph, think of either a math function OR a real-world situation where the domain would apply. Explain why your math function OR real-world situation must have the domain you identified.

Test Review

Topics to Study1) Basic Functions and their Shapes/Characteristics2) Finding Key Points on the Graphs of Functions3) Transformations4) Domain

Assessment

Warm-up

Finding the Rate of Change of Different Functions

Calculate the average rate of change between f(0) and f(5) for each of the functions f(x) = 2x + 20 and f(x) = 20(2) . Explain the similarities and differences between the functions. What causes the differences?

x

Regression Equations

Copy and graph the following tables (think about how to label the axes - glue the graph paper into your notebooks, and leave some room in between them to write notes):

x

y

x

y

2018161412108

71768178726452

200820062004200220001998

3.773.203.013.002.892.65

Writing Equations for Best-Fit Functions

Pearson 2 - 5 Example #3

Pearson 4 - 3 Example #3

Argumentation

1) 54% of a high school's students passed the Algebra 1 EOC in 2004. In 2011, 82% of the students passed. Assuming continued linear growth, what percentage of the students will pass in 2012? 2015? 2025? Do these answers make sense? Why or why not?

2) 54% of a high school's students passed the Algebra 1 EOC in 2004. In 2011, 82% of the students passed. Assuming continued exponential growth, what percentage of the students will pass in 2012? 2015? 2025? Do these answers make sense? Why or why not?

3) Compare your answers to the first two questions. What are the similarities and differences between the questions AND answers? Explain why these differences occur.

Warm-up

Common Differences/Finding Functions

x

y

3210-1-2-3

-79115-3-7-1

Pearson 5-1 Problem #4

You try!

t

d

3210-1-2-3

-264-280-270-240-196-144-90

The following table represents the depth of a submarine (t = 0 is right now - negative t values are in the past). Find the degree and function that represent the submarine's depth after t seconds.

How deep will the submarine be after 8 seconds?

Determining Functions

Every Wednesday during the summer, your local community center has to refill its pool. It raises the water level by 0.75 in/min. If a graph of the pool depth shows that the 5-foot line is reached after 20 minutes, what is the y-intercept of the graph?

Within your groups, determine the answer three ways: using a table, using an equation, and using a graph.

Which is the easiest way to solve? Why?

Write and graph a linear, quadratic, and cubic function that each have a y-intercept at 3. What are the similarities and differences between their graphs? Analyze and explain the rationale for any similarities and differences.

Argumentation

Warm- up: Equations ReviewSolve for x.

1) 5x + 8 = 49 2) 3(2x - 4) + 2 = 13 3) 4x + 3 = 9x - 12

Solving Literal Equations

1. The formula for the area of a triangle is: A = bh 2

If the area of a triangle is 60 cm , and the base of the triangle is 40 cm, what is the height?2

Method 1 (Substitute) Method 2 (Literal Equation)

2. The Pythagorean Theorem is often written as: a + b = c .2 2 2

Solving Literal Equations

18

13

a Find a.

Method 2 (Literal Equations)Method 1 (Substitute and Solve)

d = rt (VERY important equation!)

Argumentation Project

Have students research a math formula used by professionals in the scientific, medical, economic, architectural, or other field.

1. What can professionals in the field use their formula to learn or solve for?

2. What does each variable stand for?

3. Choose a different variable and solve the equation for that variable. Explain why your new equation would be beneficial to a professional in that field.

Warm-up

Vocabulary

Absolute Value -

Tolerance -

Extraneous Solutions -

Distance from zero on a number line (always positive)

Amount of error of difference allowed from the average/mean

Solutions that solve an equation but do not result in a true statement

Absolute Value Inequalities (pg. 11)

http://politicalticker.blogs.cnn.com/2011/09/01/new-cnn-poll-65-give-obama-thumbs-down-on-economy/#more-173186

According to the poll, released Wednesday morning, 28 percent of people questioned say things are going well in the country today.

The CNN/ORC International Poll was conducted August 24-25, with 1,017 adult Americans questioned by telephone. The survey's overall sampling error is plus or minus three percentage points.

Variable/ _ Ideal/ Tolerance/Actual Mean Error

Absolute Value Inequalities

The web site www.disabled-world.com states that healthy blood pressure is between 103 and 115. Represent this as an absolute value inequality.

Variable/ _ Ideal/ Tolerance/Actual Mean Error

Solving Absolute Value Equations

1) 3 -4x + 10 = 15 2) 5x - 10 + 3 = 2x - 12

Absolute Value Inequalities

1) 6x + 3 > 12 2) -3x - 9 < -12

Independent/Group Work

Argumentation

Explain why x + 5 = 2 has no solution.

Paideia Warm-up/Text

Graphing Substitution Elimination Elimination

r + 3s = 72r - s = 7

3x + 2y = 63x - y = -3

x + 12y = 68x = 8y - 12

y = x - 1y = -x + 3

Paideia Seminars1. Guidelines: - Don't raise hands, but be respectful with speech - Refer to the text and examples - Refer to other participants' comments - Apply group norms to whole class discussion

2. Goal setting: - Personal goal (Write it down!)

- Class goal

Opening Question

You have learned how to use graphing, substitution, and elimination to solve systems of equations. Based on what we discussed, how you would solve each of the following systems?

y = x - 2 y = -2x + 7

y = xy = 2x + 1

4x + 2y = 7y = 5x

4x + 2y = 46x + 2y = 8

2x + 3y = 125x - y = 13

Paideia Post-Write (On separate paper)

For each of the 5 systems we discussed today in the Paideia:1. Solve using any method you choose.

2. IN WORDS, write out the steps you used to solve it AND WHY you chose that method.

3. For each process (graphing, substitution, and elimination), write AND solve another system of equations that you would solve using each process. (You are writing three systems total.)