monday: announcements unit 5 retest: deadline is friday at 8:35am. must have test correction...
TRANSCRIPT
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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
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Algebra 2
Fall Semester Exam Review
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Test Format
• Final Exam is all calculator
• 34 Questions
• All Multiple Choice
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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)
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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
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Key Concepts on Test
• Writing Quadratic Equations– Vertex Point and another Point– Solutions and another Point– Quadratic Regression
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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)
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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
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In Class Review: Today
• Equations and Inequalities
• Relations/Functions
• Domain/Range
• Variations
• Transformations
• Data Analysis/Regression
• Quadratic Word Problems
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2( 4) 4( 6)x x
2 8 4 24x x
2 4 24 8x x
6 16x
16 8
6 3x
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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.
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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.
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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
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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
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8
6
4
2
-2
-4
-6
-8
-10 -5 5 10
Domain( , )
Range[2, )
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6
4
2
-2
-4
-6
-5 5
Domain( ,3]
Range[1, )
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Domain( , )
Range[0, )
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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)
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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
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Inverse Variation
As one variable increases, the other decreases. (or vice versa)
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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
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( )y af x c d
xR
VS or VC
R y
(+) Left
(-) Right
(+) Up
(-) Down
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Example 1
( ) 5 3f x x
5 , 3Right Up
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Example 2
( ) 2 1f x x
2 , , 1yLeft R Down
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Example 3
( ) 2 | 3 | 7f x x
3 , 2, , 7xR VS R U
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Domain( , )
Range[0, )
2, 2L VS
Transformations
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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”
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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
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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
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Window
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Max Height
Max Distance
(Vertex Pt)
(Zero)
290.7
573.9