Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic...

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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

Transcript of Graphing Quadratic Equations or Functions in the form (y ... Graphing Quadratic...Graphing Quadratic...

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

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November 25, 2017

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     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

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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

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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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

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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  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

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November 25, 2017

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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

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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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

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November 25, 2017

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­5

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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

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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

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November 25, 2017

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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

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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

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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

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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

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November 25, 2017

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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

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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

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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

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November 25, 2017

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­4

1 2

y

­4 ­1­2

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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

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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

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November 25, 2017

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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

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November 25, 2017

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  axis of symmetry

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