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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.


__________________________________________________________________

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.


__________________________________________________________________

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


3. Graph


4. Graph


x

y

x

y

x

y

x

y

5. Graph


6. Graph


7. Graph


8. Graph


9. Graph

x

y

x

y

x

y

x

y


10. Graph


11. Write the equation of the function graphed.





x

y

x

y

x

y

x

y

x

y

x

y





x

y

x

y

x

y

x

y

x

y

Test Review –Complex Numbers

Modeling Data with Quadratic Functions:

16

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