jeff bivin -- lzhs last updated: april 7, 2011 by: jeffrey bivin lake zurich high school...

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Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School [email protected]

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Page 1: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHSLast Updated: April 7, 2011

By: Jeffrey BivinLake Zurich High School

[email protected]

Page 2: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

y = 3x2 + 24x + 53

y = 3(x2 + 8x ) + 53

y + 48 = 3(x2 + 8x + (4)2) + 53

y = 3(x + 4)2 + 5

Axis of symmetry: x = -4

Vertex: (-4, 5)

y = 3(x2 + 8x + (4)2) + 53 - 48

3●(4)2 = 48

x + 4 = 0

Note: opens up

Page 3: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabolay = 3(x + 4)2 + 5

No x-intercept

y-intercept:

23 0 24 0 53 53y

x-intercept

none

y-intercept

0, 53

Page 4: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

y = -2x2 + 12x + 11

y = -2(x2 - 6x ) + 11

y - 18 = -2(x2 - 6x + (-3)2) + 11

y = -2(x - 3)2 + 29

Axis of symmetry: x = 3

Vertex: (3, 29)

y = -2(x2 - 6x + (-3)2) + 11 + 18

-2●(-3)2 = -18

x - 3 = 0

Note: opens down

Page 5: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabolay = -2(x - 3)2 + 29

x-intercept

y-intercept

22 0 3 29y

0, 11

20 2 3 29x

229 2 3x

2292 3x

292 3x

2923 x

5823 , 0

36.808, 0 & .808, 0

11y

Page 6: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

x = -2y2 - 8y - 1

x = -2(y2 + 4y ) - 1

x - 8 = -2(y2 + 4y + (2)2) - 1

x = -2(y + 2)2 + 7

Axis of symmetry: y = -2

Vertex: (7, -2)

x = -2(y2 + 4y + (2)2) - 1 + 8

-2(2)2 = -8

y + 2 = 0

Note: opens left

Page 7: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabolax = -2(y + 2)2 + 7

y-intercepty-intercept

22 0 2 7x

1, 0

20 2 2 7y

27 2 2y

272 2y

72 2y

722 y

1420, 3

4.871, 0 & 1.129, 0

8 7x

Page 8: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

x = y2 - 4y + 11

x = (y2 - 8y ) + 11

x + 8 = (y2 - 8y + (-4)2) + 11

x = (y - 4)2 + 3

Axis of symmetry: y = 4

Vertex: (3, 4)

x = (y2 - 8y + (-4)2) + 11 - 82

12

12

1

2

1

2

1

8)16(2

1

y - 4 = 0

Note: opens right

Page 9: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola 21

4 32

x y

y-interceptx-intercept

210 4 3

2x

11, 0

none

8 3x 11x

Page 10: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

x = y2 + 10y + 8

x = (y2 + 10y ) + 8

x + 25 = (y2 + 10y + (5)2) + 8

x = (y + 5)2 - 17

Axis of symmetry: y = -5

Vertex: (-17, -5)

x = (y2 + 10y + (5)2) + 8 - 25

(5)2 = 25

y + 5 = 0

Note: opens right

Page 11: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabolax = (y + 5)2 - 17

y-interceptx-intercept

20 5 17x

8, 0

20 5 17y

217 5y

17 5y

5 17 y

0, 5 17

0.877, 0 & 9.123, 0

25 17x 8x

Page 12: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabola

y = 5x2 - 30x + 46

y = 5(x2 - 6x ) + 46

y + 45 = 5(x2 - 6x + (-3)2) + 46

y = 5(x - 3)2 + 1

Axis of symmetry: x = 3

Vertex: (3, 1)

y = 5(x2 - 6x + (-3)2) + 46 - 45

5●(-3)2 = 45

x - 3 = 0

Note: opens up

Page 13: Jeff Bivin -- LZHS Last Updated: April 7, 2011 By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org

Jeff Bivin -- LZHS

Graph the following parabolay = 5(x - 3)2 + 1

x-intercept y-intercept

25 0 3 1y

0, 46

none

45 1y