Transcript Algebra 2
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( x 4) 4( x 6)
2x 8 4x 24
2x 4x 24 8
6x 16
16 8
x
6 3
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.
ANSWER
The solutions are all real numbers less than 3. The
graph is shown below.
Relations
Ordered Pairs
(2, 3)
(-3, 1)
(1, -2)
Graphs
Tables
X
2
-3
1
Y
3
1
-2
X
Mapping
Y
2
3
-3
1
1
-2
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
Domain
6
(, )
4
Range
2
[2, )
-5
5
-2
Domain
6
4
(,3]
Range
[1, )
2
-5
5
Domain
(, )
Range
[0, )
Direct Variation
As one variable increases, the other
must also increase ( up, up)
OR
As 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.
y1 y2
x1 x2
y1 8
6 2
2 y1 48
y1 24
Inverse Variation
As one variable increases, the other
decreases. (or vice versa)
Inverse Variation
Find x when y = 5, if y varies inversely as x and
x = 6 when y = -18.
x1 y1 x2 y2
x1 21.6
x1 5 6 18
5x1 108
y af ( x c) d
Rx
VS or VC
Ry
(+) Up
(-) Down
(+) Left
(-) Right
Example 1
f ( x) x 5 3
Right 5 , Up 3
Example 2
f ( x) x 2 1
Left 2 , Ry , Down 1
Example 3
f ( x) 2 | x 3 | 7
R 3 , VS 2, Rx , U 7
Domain
(, )
Transformations
Range
L 2, VS 2
[0, )
Data Analysis
Height
(meters)
15
30
45
60
75
90
105
Distance
Km
13.833
19.562
23.959
27.665
30.931
33.883
36.598
STAT Plotter “ON”
Zoom 9
What Parent Function??
Weeks
Experience
4
7
8
1
6
3
5
2
9
6
Speed
(wpm)
33 45 49 20 40 30 38 22 52 44 42
y-axis
45
40
35
30
25
y 4.064 x 16.300
20
15
10
r .986
5
0
1
2
3
4
5
6
7
8
9
10
x-axis
7
Application Problems
y .0035 x 2 x 5
2
• Need to change the
viewing WINDOW
• x-min, x-max
• y-min, y-max
Put in Calculator
Window
Max Height (Vertex Pt)
290.7
Max Distance
(Zero)
573.9