monday: announcements unit 5 retest: deadline is friday at 8:35am. must have test correction...

Monday: Announcements• Unit 5 Retest: Deadline is Friday at 8:35am.

• Must have test correction complete to retest and come to at least one tutorial session for help.

• Dropping Lowest Grade (40% category)!

• Final Exam Review will be graded and is the last grade for the 3rd 6 weeks

• Answer key is posted on-line, but you MUST show work to get credit.

• No Factoring Quiz this week due to Final Exams

Algebra 2

Fall Semester Exam Review

Test Format

• Final Exam is all calculator

• 34 Questions

• All Multiple Choice

Key Concepts on Test• Solving Equations and Inequalities• Domain/Range/Functions• Parent Function graphs• Direct and Inverse Variation problems• Transformations

– Order of transformations– Graphing using transformations

• Linear Regression (STAT)• Data Analysis (zoom 9)

Key Concepts on Test

• Quadratic Equations– Simplify positive and negative radicals– Graphing (vertex point, AOS, solutions)– Factoring Methods– Square Roots Method– Complete the Square– Discriminant– Quadratic Formula

• Vertex Format/Complete the Square

Key Concepts on Test

• Writing Quadratic Equations– Vertex Point and another Point– Solutions and another Point– Quadratic Regression

Calculator

• Can be used to solve 60% of your test

• Know the following:– How to graph– 2nd trace (vertex and zeros)– Linear & quadratic regressions– Plug in numbers (watch out for negatives)

Testing Hints

• If you can graph it in the calculator, then do so

• Double graphing to compare

• Be careful of negatives when solving equations

• Questions with graphs! Look carefully at each graph so you select the one you really want

• Plug in solutions to calculator to check

In Class Review: Today

• Equations and Inequalities

• Relations/Functions

• Domain/Range

• Variations

• Transformations

• Data Analysis/Regression

• Quadratic Word Problems

2( 4) 4( 6)x x

2 8 4 24x x

2 4 24 8x x

6 16x

16 8

6 3x

BIG DIFFERENCE

If you multiply or divide each side of an inequality by a negative number then the order of the inequality must be switched.

EXAMPLE 4 Solve an inequality with a variable on both sides

Solve 5x + 2 > 7x – 4. Then graph the solution.

5x + 2 > 7x – 4

– 2x + 2 > – 4

– 2x > – 6

x < 3

Write original inequality.

Subtract 7x from each side.

Subtract 2 from each side.Divide each side by – 2 and reverse the inequality.

ANSWERThe solutions are all real numbers less than 3. The graph is shown below.

RelationsOrdered Pairs

(2, 3)

(-3, 1)

(1, -2)

X Y

2 3

-3 1

1 -2

Tables

GraphsMapping

2

-3

1

3

1

-2

X Y

Example :

• Given the following ordered pairs, find the domain and range. Is it a function

• {(4,5), (-2,3), (5,6)}

• Domain is {-2, 4, 5}

• Range is {3, 5, 6}

• YES, no duplicated x-values

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Domain( , )

Range[2, )

6

4

2

-2

-4

-6

-5 5

Domain( ,3]

Range[1, )

Domain( , )

Range[0, )

Direct Variation

As one variable increases, the other must also increase ( up, up)

ORAs one variable decreases, the other variable must also decrease. (down,

down)

Direct Variation

• Find y when x = 6, if y varies directly as x and y = 8 when x = 2.

1 2

1 2

y y

x x 1 8

6 2

y 12 48y

1 24y

Inverse Variation

As one variable increases, the other decreases. (or vice versa)

Inverse VariationFind x when y = 5, if y varies inversely as x and x = 6 when y = -18.

1 1 2 2x y x y1 5 6 18x

15 108x 1 21.6x

( )y af x c d

xR

VS or VC

R y

(+) Left

(-) Right

(+) Up

(-) Down

Example 1

( ) 5 3f x x

5 , 3Right Up

Example 2

( ) 2 1f x x

2 , , 1yLeft R Down

Example 3

( ) 2 | 3 | 7f x x

3 , 2, , 7xR VS R U

Domain( , )

Range[0, )

2, 2L VS

Transformations

Data Analysis

Height(meters)

15 30 45 60 75 90 105

DistanceKm

13.833 19.562 23.959 27.665 30.931 33.883 36.598

Zoom 9

What Parent Function??

STAT Plotter “ON”

Weeks Experience

4 7 8 1 6 3 5 2 9 6 7

Speed (wpm)

33

45

49

20

40

30

38 22 52 44 42

1 2 63 4 5 7 8 9 10

20

15

10

5

35

2530

40

45

x-axis

y-axis

0

4.064 16.300y x

.986r

Application Problems

• Need to change the viewing WINDOW

• x-min, x-max• y-min, y-max

2.0035 2 5y x x Put in Calculator

Window

Max Height

Max Distance

(Vertex Pt)

(Zero)

290.7

573.9