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Algebra 2 Notes Packet – Quadratic FunctionsSection/SOL
TopicAssignment: Date Due: Grade:
5-6AII.3
Complex Numbers Page 274: 2-18 even, 30-40 evenClasswork- page 4
Quiz on 5-65-1AII.9
Modeling Data with Quadratic Functions
Pages 237-238: 2-28 even
Quiz on 5-15-2 and 5-3AII.6,7
Graphing Parabolas Page 251: 1-12 all
Writing Equations from Graphs of Parabolas
Pages 251-252: 13-26 all
Quiz on 5-3
Review and Test – Unit 5
Notes - 5.6 Complex Numbers
Pure Imaginary Numbers:
The imaginary number, , is defined as the number whose square is -1.
And
= ____________________________
Example 1 Simplify:
a) b) c)
Powers of : I won! I won! (negative, negative)
Example 2 – Simplify
a) b) c) d)
You Try:
1. 2. 3.
4. 5. 6.
Complex Numbers : Can be written in the form
Example 3 – Simplify:
Example 4 – Simplify:
You Try with Complex Numbers:
1. 2.
3. 4.
Classwork 5-6:
Notes 5-1 Modeling Data with Quadratic Functions
Warm-up: Simplify.
1. 2. 3.
4. 5.
Definition: A quadratic function is a function that can be written in the standard form
where
Example 1: Determine whether each function is linear or quadratic. Identify the
quadratic, linear and constant terms.
a) b)
The graph of a quadratic function is a parabola. The axis of symmetry is the line that
divides a parabola into two parts that are mirror images. The vertex of the parabola is
the maximum or minimum value of the function. The axis of symmetry and the vertex
have the same x-values. Each point of the parabola has a corresponding point on its
mirror image.
Example 2: Identify the vertex and the axis of symmetry. Identify points corresponding
to P and Q.
Modeling Data with Quadratic Functions:
Example 3: Find a quadratic function to model the values in the table:
x Y
2 3
3 13
4 29
Example 4: The table below shows the height of a column of water as it drains from its
container. Model the data with a quadratic function. Use the model to estimate the
water level at 35 seconds.
Elapsed time,
seconds
Water level,
mm
0 120
10 100
20 83
30 66
40 50
50 37
60 28
------------------------------------------------------------------------------------------------------------
You Try: Find a quadratic model for each set of values.
1. 2.
3. Price of a First-Class Stamp:
Year 1974 1978 1981 1983 1988 1995 2001 2002
Price(cents
)
10 15 18 20 25 32 34 37
a) Estimate when first class postage was $0.29.
b) Predict when first class postage will be $0.50.
5-2 and 5-3 Notes: Graphing Parabolas
Standard Form: Parent graph:
I. Graph the parabolas with different values of “H”:1. 2. 3.
1. How are graphs 1, 2, and 3 similar to the parent graph? _____________________
__________________________________________________________________
2. How are graphs 1, 2, and 3 differ from the parent graph? ____________________
__________________________________________________________________
3. How does “H” affect the total graph? ___________________________________
__________________________________________________________________
II. Graph these parabolas that have different values for “K”:4. 5. 6.
1. How are graphs 4, 5, and 6 similar to the parent graph? _____________________
__________________________________________________________________
2. How are graphs 4, 5, and 6 differ from the parent graph? ____________________
__________________________________________________________________
3. How does “K” affect the total graph? ___________________________________
III. Graph these parabolas that have different values for “A”:
7. 8. 9.
1. How are graphs 7, 8, and 9 similar to the parent graph? _____________________
__________________________________________________________________
2. How are graphs 7, 8, and 9 differ from the parent graph? ______________________________________________________________________________________
3. How does “A” affect the total graph? ___________________________________IV. Summary
If the standard form for the parabola is , tell how A, H, and K affect the vertex and the size of the graph. ________________________________________
__________________________________________________________________
__________________________________________________________________
V. Without graphing, compare the graph of the equation listed to the parent graph, . Describe the translation (left/right, up/down), type of opening (up or down, fat or
skinny).
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
5-2 and 5-3 Notes-Writing Equations of Parabolas from Graphs:
1. 2. 3.
vertex: __________
vertex: __________ vertex: __________A = __________ A = __________ A = __________Equation: Equation: Equation:
________________ ________________ ________________
4. 5. 6.
vertex: __________ vertex: __________ vertex: __________A = __________ A = __________ A = __________Equation: Equation: Equation:
________________ ________________ ________________
Test Review - Graphing Parabolas
1. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
2. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
3. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
4. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
x
y
x
y
x
y
x
y
5. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
6. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
7. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
8. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
9. Graph
x
y
x
y
x
y
x
y
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
10. Graph
Domain: _____________________Range: ______________________Increasing on: _________________Decreasing on: ________________
11. Write the equation of the function graphed.
12. Write the equation of the function graphed.
13. Write the equation of the function graphed.
14. Write the equation of the function graphed.
15. Write the equation of the function graphed.
x
y
x
y
x
y
x
y
x
y
x
y
16. Write the equation of the function graphed.
17. Write the equation of the function graphed.
18. Write the equation of the function graphed.
19. Write the equation of the function graphed.
x
y
x
y
x
y
x
y
x
y
Test Review –Complex Numbers
Modeling Data with Quadratic Functions:
16