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Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 1 November 25, 2017 Nov 1911:01 AM Graphing Quadratic Equations or Functions in the form : or

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Page 1: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

1

November 25, 2017

Nov 19­11:01 AM

     Graphing Quadratic             

   Equations or Functions

        in the form :

or

Page 2: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

2

November 25, 2017

Nov 4­11:04 AM

y

xx­interceptx­intercept

y­interceptvertex

axis ofsymmetry

Page 3: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

3

November 25, 2017

Nov 4­11:05 AM

y

xx­interceptx­intercept

y­interceptvertex

axis ofsymmetry

Page 4: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

4

November 25, 2017

Nov 4­11:05 AM

To find the y­coordinate of the vertex, substitute the x­coordinateof the vertex into the equation, and simplify. 

Page 5: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

5

November 25, 2017

Nov 4­1:54 PM

Page 6: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

6

November 25, 2017

Nov 4­11:05 AM

Page 7: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

7

November 25, 2017

Nov 4­3:43 PM

EXAMPLE 1

Page 8: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

8

November 25, 2017

Nov 4­3:44 PM

To find the y­coordinate of the vertex, substitute the x­coordinate of the vertex into the equation, and simplify. 

Page 9: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

9

November 25, 2017

Nov 4­3:44 PM

Page 10: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

10

November 25, 2017

Nov 4­3:44 PM

Page 11: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

11

November 25, 2017

Nov 4­3:44 PM

Page 12: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

12

November 25, 2017

Nov 4­4:41 PM

7

7­1

16

y

3

x

Page 13: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

13

November 25, 2017

Nov 4­5:17 PM

Connect the ordered pairs with 

U­shaped curve.a smooth 

7

7­1

16

y

x3

Page 14: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

14

November 25, 2017

Nov 4­4:34 PM

Page 15: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

15

November 25, 2017

Nov 4­4:52 PM

  axis of symmetry

7

7­1

16

y

x3

Page 16: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

16

November 25, 2017

Nov 4­5:18 PM

EXAMPLE 2

Page 17: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

17

November 25, 2017

Nov 5­6:52 AM

To find the y­coordinate of the vertex, substitute the x­coordinate of the vertex into the equation, and simplify. 

Page 18: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

18

November 25, 2017

Nov 5­6:54 AM

Page 19: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

19

November 25, 2017

Nov 5­6:57 AM

Page 20: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

20

November 25, 2017

Nov 5­6:58 AM

Page 21: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

21

November 25, 2017

Nov 5­7:02 AM

Page 22: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

22

November 25, 2017

Nov 5­7:10 AM

43

3

­5

1 2

y

x

Page 23: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

23

November 25, 2017

Nov 5­7:12 AM

Connect the ordered pairs with 

U­shaped curve.a smooth 

43

3

­5

1 2

y

Page 24: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

24

November 25, 2017

Nov 5­7:18 AM

Page 25: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

25

November 25, 2017

Nov 5­7:32 AM

43

3

­5

1 2

y

  axis of symmetry

Page 26: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

26

November 25, 2017

Nov 5­7:41 AM

EXAMPLE 3

Page 27: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

27

November 25, 2017

Nov 5­7:42 AM

To find the y­coordinate of the vertex, substitute the x­coordinate of the vertex into the equation, and simplify. 

Page 28: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

28

November 25, 2017

Nov 5­9:06 AM

Page 29: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

29

November 25, 2017

Nov 5­9:12 AM

Page 30: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

30

November 25, 2017

Nov 5­9:13 AM

Page 31: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

31

November 25, 2017

Nov 5­9:16 AM

43

­4

1 2

y

­4 ­1­2

­7

Page 32: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

32

November 25, 2017

Nov 5­9:16 AM

43

­4

1 2

y

­4 ­1­2

­7

Page 33: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

33

November 25, 2017

Nov 5­9:32 AM

Page 34: Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic Equations or Functions in the form (y = ax^2 + bx + c).notebook 8 November 25,

Graphing Quadratic Equations or Functions in the form (y  = ax^2 + bx + c).notebook

34

November 25, 2017

Nov 5­2:12 PM

  axis of symmetry

43

­4

1 2

y

­4 ­1­2

­7